Shaped abrasive particles and methods of forming same

ABSTRACT

A method of forming a shaped abrasive particle includes having a body formed by an additive manufacturing process.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of U.S. patent application Ser. No.15/679,427, entitled “SHAPED ABRASIVE PARTICLES AND METHODS OF FORMINGSAME,” by Adam J. STEVENSON et al., filed Aug. 17, 2017, which is acontinuation of U.S. patent application Ser. No. 14/502,562, entitled“SHAPED ABRASIVE PARTICLES AND METHODS OF FORMING SAME,” by Adam J.STEVENSON et al., filed Sep. 30, 2014, now granted as U.S. Pat. No.9,783,718, granted Oct. 10, 2017, which claims priority under 35 U.S.C.§ 119(e) to U.S. Patent Application No. 61/884,474, entitled “SHAPEDABRASIVE PARTICLES AND METHODS OF FORMING SAME,” by Adam J. STEVENSON etal., filed Sep. 30, 2013, which are all assigned to the current assigneehereof and incorporated herein by reference in their entireties.

BACKGROUND Field of the Disclosure

The following is directed to shaped abrasive particles and, moreparticularly, to a process of forming shaped abrasive particles using anadditive manufacturing process.

Description of the Related Art

Abrasive articles incorporating ceramic articles such as abrasiveparticles are useful for various material removal operations includinggrinding, finishing, polishing, and the like. Depending upon the type ofabrasive material, such abrasive particles can be useful in shaping orgrinding various materials in the manufacturing of goods. Certain typesof abrasive particles have been formulated to date that have particulargeometries, such as triangular shaped abrasive particles and abrasivearticles incorporating such objects. See, for example, U.S. Pat. Nos.5,201,916; 5,366,523; and 5,984,988.

Previously, three basic technologies have been employed to produceabrasive particles having a specified shape, including fusion,sintering, and chemical ceramic. In the fusion process, abrasiveparticles can be shaped by a chill roll, the face of which may or maynot be engraved, a mold into which molten material is poured, or a heatsink material immersed in an aluminum oxide melt. See, for example, U.S.Pat. No. 3,377,660. In sintering processes, abrasive particles can beformed from refractory powders having a particle size of up to 10micrometers in diameter. Binders can be added to the powders along witha lubricant and a suitable solvent to form a mixture that can be shapedinto platelets or rods of various lengths and diameters. See, forexample, U.S. Pat. No. 3,079,242. Chemical ceramic technology involvesconverting a colloidal dispersion or hydrosol (sometimes called a sol)to a gel or any other physical state that restrains the mobility of thecomponents, drying, and firing to obtain a ceramic material. See, forexample, U.S. Pat. Nos. 4,744,802 and 4,848,041.

Rudimentary molding processes have been disclosed as potentially usefulin forming limited shaped abrasive particles, such as those disclosed inU.S. Pat. Nos. 5,201,916, 5,366,523, 5,584,896, and U.S. Pat. Publs.2010/0151195, 2010/0151196. Other processes of forming shaped abrasiveparticles have been disclosed, see for example, U.S. Pat. Nos.6,054,093, 6,228,134, 5,009,676, 5,090,968, and 5,409,645.

The industry continues to demand improved abrasive materials andabrasive articles including shaped abrasive particles.

SUMMARY

According to one aspect, a method of forming a shaped abrasive particleincludes having a body formed by an additive manufacturing process.

According to a second aspect, a method includes forming a body of ashaped abrasive particle according to a digital model.

In yet another aspect, a method of forming a fixed abrasive includesforming a plurality of shaped abrasive particles on a substrate, whereineach of the shaped abrasive particles of the plurality of shapedabrasive particles have a body formed by an additive manufacturingprocess.

According to another aspect, a shaped abrasive particle includes a bodyhaving at least one major surface having a self-similar feature.

For still another aspect, a shaped abrasive particle has a body havingat least one peripheral ridge extending around at least a portion of aside surface of the body.

In one aspect, a shaped abrasive particle has a body having at least onemajor surface defining a concave stepped surface.

For another aspect, a shaped abrasive particle has a body having atleast one transverse ridge extending along at least two surfaces and anadjoining edge between the at least two surfaces.

According to one aspect, a shaped abrasive particle includes a bodyhaving a corner including a plurality of microprotrusions extending fromthe corner.

For still another aspect, a shaped abrasive particle has a bodyincluding a surface comprising a scalloped topography.

According to another aspect, a method of forming a shaped abrasiveparticle includes using a low pressure injection molding process.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure may be better understood, and its numerousfeatures and advantages made apparent to those skilled in the art, byreferencing the accompanying drawings. Embodiments are illustrated byway of example and are not limited in the accompanying figures.

FIG. 1A includes a perspective view illustration of a method of forminga portion of a shaped abrasive particle in accordance with anembodiment.

FIG. 1B includes an illustration of a system and method of forming aportion of a shaped abrasive particle in accordance with an embodiment.

FIG. 1C includes an illustration of a filling pattern according to anembodiment.

FIG. 1D includes an illustration of filling pattern according to anembodiment.

FIG. 1E includes an illustration of an end of a nozzle according to anembodiment.

FIG. 2 includes a perspective view illustration of an abrasive articleincluding shaped abrasive particles according to an embodiment.

FIG. 3 includes a side view of a shaped abrasive particle and percentageflashing according to an embodiment.

FIG. 4 includes a cross-sectional illustration of a portion of a coatedabrasive article according to an embodiment.

FIG. 5 includes a cross-sectional illustration of a portion of a coatedabrasive article according to an embodiment.

FIGS. 6-19 include illustrations of shaped abrasive particles accordingto an embodiment.

FIG. 20 includes a perspective view illustration of a shaped abrasiveparticle according to an embodiment.

FIG. 21 includes a top view of a major surface of the shaped abrasiveparticle of FIG. 20.

FIG. 22 includes a top view image of a portion of the shaped abrasiveparticle of FIG. 20.

FIG. 23 includes a portion of a major surface of the shaped abrasiveparticle of FIG. 20.

FIG. 24 includes a side view image of a portion of a shaped abrasiveparticle according to an embodiment.

FIG. 25 includes an image of a portion of a corner of a shaped abrasiveparticle according to an embodiment herein.

FIG. 26 includes an image of a portion of a surface of a shaped abrasiveparticle having a scalloped topography according to an embodiment.

FIG. 27 includes a top-down image of a shaped abrasive particleaccording to an embodiment.

FIG. 28 includes a top-down view of a shaped abrasive particle accordingto an embodiment.

FIG. 29 includes a side-view image of the shaped abrasive particle ofFIG. 28.

FIG. 30 includes an image of a corner of a shaped abrasive particleaccording to an embodiment.

The use of the same reference symbols in different drawings indicatessimilar or identical items. Further, skilled artisans appreciate thatelements in the figures are illustrated for simplicity and clarity andhave not necessarily been drawn to scale. For example, the dimensions ofsome of the elements in the figures may be exaggerated relative to otherelements to help to improve understanding of embodiments of theinvention.

DETAILED DESCRIPTION

The following is generally directed to a method of forming a shapedabrasive particle utilizing an additive manufacturing process. Theshaped abrasive particles can be used in a variety of industriesincluding, but not limited to, automotive, medical, construction,foundry, aerospace, abrasives, and the like. Such shaped abrasiveparticles may be utilized as free abrasive particles or incorporatedinto fixed abrasive articles including, for example, coated abrasivearticles, bonded abrasive articles, and the like. Various other uses maybe derived for the shaped abrasive particles.

In accordance with one aspect, the shaped abrasive particles of theembodiments herein can be formed to have a body formed by an additivemanufacturing process. As used herein, an “additive manufacturingprocess” includes a process, wherein the body of the shaped abrasiveparticle can be formed by compiling a plurality of portions together ina particular orientation with respect to each other such that, when theplurality is compiled, each of the discrete portions can define at leasta portion of the shape of the body. Moreover, in particular instances,the additive manufacturing process can be a template-free process,wherein the material being manipulated to form discrete portions, andultimately the body itself, need not be placed within a template (e.g.,a mold). Rather, the material being manipulated can be deposited indiscrete portions, wherein each of the discrete portions has acontrolled dimension such that when the plurality is compiled, the bodyalso has a controlled dimension. Therefore, unlike typical moldingoperations, additive manufacturing processes of the embodiments hereinmay not necessarily need to incorporate a template that is configured tocontain the material being manipulated to form the body.

In particular instances, an additive manufacturing process that is usedto form a shaped abrasive particle can be a prototype printing process.In more particular instances, the process of forming the shaped abrasiveparticle can include a prototype printing of a body of the shapedabrasive particle, where the shaped abrasive particle includes a shapedabrasive particle or a precursor shaped abrasive particle. In otherinstances, the additive manufacturing process may include or beconsidered a laminated object manufacturing process. In the laminatedobject manufacturing process, individual layers may be formed discretelyand joined together to form the body of the shaped abrasive particle.

In accordance with an embodiment, the method of forming a shapedabrasive particle having a body formed by an additive manufacturingprocess can include deposition of a first print material as a firstportion of the body at a first time, and deposition of a second printmaterial as a second portion of the body distinct from the first portionat a second time. It will be understood that the first time can be thesame as, or different from, the second time. More particularly, thefirst print material in some instances may include a solid material, apowder, a solution, a mixture, a liquid, a slurry, a gel, a binder, andany combination thereof. In one particular instance, the first printmaterial can include a sol gel material. For example, the first printmaterial can include a mixture, where the mixture can be a gel formed ofa powder material and a liquid, and where the gel can be characterizedas a shape-stable material having the ability to substantially hold agiven shape even in the green (i.e., unfired) state. In accordance withan embodiment, the gel can be formed of the powder material as anintegrated network of discrete particles. In particular instances, themixture can include a sol-gel material, which may have one or moreparticulate materials forming a matrix of the mixture. The particulatematerials can include any of the materials noted herein, such as theceramic materials.

The first print material may have a certain content of solid material,liquid material, and additives such that it has suitable rheologicalcharacteristics for use with the process detailed herein. That is, incertain instances, the first print material can have a certainviscosity, and more particularly, suitable rheological characteristicsthat form a dimensionally-stable phase of material that can be formedthrough the process as noted herein. A dimensionally-stable phase ofmaterial can be a material that can be formed to have a particular shapeand substantially maintain the shape for at least a portion of theprocessing subsequent to forming. In certain instances, the shape may beretained throughout subsequent processing, such that the shape initiallyprovided in the forming process is present in the finally-formed object.

The print material, including any print material of the embodimentsherein can be a mixture and may have a particular content of aninorganic material, which may be a solid powder material or particulate,such as a ceramic powder material. In accordance with an embodiment, theprint material can include a mixture that may include an inorganicmaterial having suitable rheological characteristics that facilitateformation of the body including a shaped abrasive particle. For example,in one embodiment, the first print material can have a solids content ofat least about 25 wt %, such as at least about 35 wt %, at least about36 wt %, or even at least about 38 wt % for the total weight of themixture. Still, in at least one non-limiting embodiment, the solidscontent of the first print material can be not greater than about 75 wt%, such as not greater than about 70 wt %, not greater than about 65 wt%, not greater than about 55 wt %, not greater than about 45 wt %, notgreater than about 44 wt %, or not greater than about 42 wt %. It willbe appreciated that the content of the solids materials in the firstprint material can be within a range between any of the minimum andmaximum percentages noted above, including for example within a range ofat least about 25 wt % and not greater than about 70 wt %, the leastabout 35 wt % and not greater than about 55 wt %, or even at least about36 wt % and not greater than about 45 wt %.

According to one embodiment, the ceramic powder material can include anoxide, a nitride, a carbide, a boride, an oxycarbide, an oxynitride, anda combination thereof. In particular instances, the ceramic material caninclude alumina. More specifically, the ceramic material may include aboehmite material, which may be a precursor of alpha alumina. The term“boehmite” is generally used herein to denote alumina hydrates includingmineral boehmite, typically being Al₂O₃.H₂O and having a water contenton the order of 15%, as well as pseudoboehmite, having a water contenthigher than 15%, such as 20-38% by weight. It is noted that boehmite(including pseudoboehmite) has a particular and identifiable crystalstructure, and therefore a unique X-ray diffraction pattern. As such,boehmite is distinguished from other aluminous materials including otherhydrated aluminas such as ATH (aluminum trihydroxide), a commonprecursor material used herein for the fabrication of boehmiteparticulate materials.

Furthermore, the print material, including any of the print materials ofthe embodiments herein, may be in the form of a mixture, may have aparticular content of liquid material. Some suitable liquids may includewater. In accordance with one embodiment, the first print material canbe formed to have a liquid content less than the solids content of themixture. In more particular instances, the first print material can havea liquid content of at least about 25 wt % for the total weight of themixture. In other instances, the amount of liquid within the first printmaterial can be greater, such as at least about 35 wt %, at least about45 wt %, at least about 50 wt %, or even at least about 58 wt %. Still,in at least one non-limiting embodiment, the liquid content of the firstprint material can be not greater than about 75 wt %, such as notgreater than about 70 wt %, not greater than about 65 wt %, not greaterthan about 62 wt %, or even not greater than about 60 wt %. It will beappreciated that the content of the liquid in the first print materialcan be within a range between any of the minimum and maximum percentagesnoted above.

Furthermore, to facilitate processing and forming shaped abrasiveparticles according to embodiments herein, the first print material, canhave a particular storage modulus. For example, the first print materialcan have a storage modulus of at least about 1×10⁴ Pa, such as at leastabout 4×10⁴ Pa, or even at least about 5×10⁴ Pa. However, in at leastone non-limiting embodiment, the first print material may have a storagemodulus of not greater than about 1×10⁷ Pa, such as not greater thanabout 2×10⁶ Pa. It will be appreciated that the storage modulus of thefirst print material can be within a range between any of the minimumand maximum values noted above.

The storage modulus can be measured via a parallel plate system usingARES or AR-G2 rotational rheometers, with Peltier plate temperaturecontrol systems. For testing, the first print material can be extrudedwithin a gap between two plates that are set to be approximately 8 mmapart from each other. After extruding the first print material into thegap, the distance between the two plates defining the gap is reduced to2 mm until the first print material completely fills the gap between theplates. After wiping away excess material, the gap is decreased by 0.1mm and the test is initiated. The test is an oscillation strain sweeptest conducted with instrument settings of a strain range between 0.01%to 100%, at 6.28 rad/s (1 Hz), using 25-mm parallel plate and recording10 points per decade. Within 1 hour after the test completes, the gap islowered again by 0.1 mm and the test is repeated. The test can berepeated at least 6 times. The first test may differ from the second andthird tests. Only the results from the second and third tests for eachspecimen should be reported.

The print material, which may include a mixture, can be formed to have aparticular viscosity to facilitate formation of the body of the shapedabrasive particle having the features of the embodiments herein. Forexample, the mixture can have a viscosity of at least about 4×10³ Pa s,such as at least about 5×10³ Pa s, at least about 6×10³ Pa s, at leastabout 7×10³ Pa s, at least about 7.5×10³ Pa s. In another non-limitingembodiment, the mixture can have a viscosity of not greater than about20×10³ Pa s, such as not greater than about 18×10³ Pa s, not greaterthan about 15×10³ Pa s, not greater than about 12×10³ Pa s. Still, itwill be appreciated that the mixture can have a viscosity within a rangeincluding any of the minimum and maximum values noted above, includingbut not limited to, at least about 4×10³ Pa s and not greater than about20×10³ Pa s, such as at least about 5×10³ Pa s and not greater thanabout 18×10³ Pa s, at least about 6×10³ Pa s and not greater than about15×10³ Pa s. The viscosity can be measured in the same manner as thestorage modulus as described above.

Moreover, the first print material, which may be in the form of amixture, may be formed to have a particular content of organic materialsincluding, for example, organic additives that can be distinct from theliquid to facilitate processing and formation of shaped abrasiveparticles according to the embodiments herein. Some suitable organicadditives can include stabilizers, binders such as fructose, sucrose,lactose, glucose, UV curable resins, and the like.

Notably, the embodiments herein may utilize a first print material thatcan be distinct from slurries used in conventional forming operations.For example, the content of organic materials within the first printmaterial and, in particular, any of the organic additives noted above,may be a minor amount as compared to other components within themixture. In at least one embodiment, the first print material can beformed to have not greater than about 30 wt % organic material for thetotal weight of the first print material. In other instances, the amountof organic materials may be less, such as not greater than about 15 wt%, not greater than about 10 wt %, or even not greater than about 5 wt%. Still, in at least one non-limiting embodiment, the amount of organicmaterials within the first print material can be at least about 0.01 wt%, such as at least about 0.5 wt % for the total weight of the firstprint material. It will be appreciated that the amount of organicmaterials in the first print material can be within a range between anyof the minimum and maximum values noted above.

Moreover, the first print material can be formed to have a particularcontent of acid or base, distinct from the liquid content, to facilitateprocessing and formation of shaped abrasive articles according to theembodiments herein. Some suitable acids or bases can include nitricacid, sulfuric acid, citric acid, chloric acid, tartaric acid,phosphoric acid, ammonium nitrate, and ammonium citrate. According toone particular embodiment in which a nitric acid additive is used, thefirst print material can have a pH of less than about 5, and moreparticularly, can have a pH within a range between about 2 and about 4.

FIG. 1A includes a perspective view illustration of a process of forminga shaped abrasive particle via an additive manufacturing process inaccordance with an embodiment. As illustrated, the additivemanufacturing process may utilize a deposition assembly 151 configuredto have multi-axial movement in at least the X-direction, theY-direction, and Z-direction for controlled deposition of a printmaterial 122. In particular instances, the deposition assembly 151 canhave a deposition head 153 configured to provide controlled delivery ofa print material to a particular position. Notably, the depositionassembly 151 may provide controlled deposition of a first print materialas a first portion of the body at a first time and deposition of asecond print material as a second portion of the body that is distinctfrom the first portion at the second time. Such a process can facilitatethe controlled deposition of discrete portions such that the discreteportions are deposited in precise locations with respect to each otherand can facilitate formation of a body of a shaped abrasive particlehaving suitable shape, dimensions, and performance.

In particular instances, the deposition assembly 151 can be configuredto deposit a first print material 102 as a first portion 101 of the bodyof the shaped abrasive particle. In particular, the first portion 101can define a fraction of the total volume of the body of the shapedabrasive particle. In particular instances, the first portion 101 canhave a first portion length (Lfp), a first portion width (Wfp), and afirst portion thickness (Tfp). According to one embodiment, Lfp may begreater than or equal to Wfp, Lfp may be greater than or equal to Tfp,and Wfp may be greater than or equal to Tfp. In particular instances,the length of the first portion may define the largest dimension of thefirst portion 101, and the width of the first portion 101 may define adimension extending in a direction generally perpendicular to the length(Lfp) and may define the second largest dimension of the first portion101. Moreover, in some embodiments, the thickness (Tfp) of the firstportion 101 may define the smallest dimension of the first portion 101,and may define a dimension extending in a direction perpendicular toeither or both of the length (Lfp) and the width (Wfp). It will beappreciated, however, that the first portion 101 can have various shapesas will be defined further herein.

In accordance with an embodiment, the first portion 101 can have aprimary aspect ratio (Lfp:Wfp) to facilitate suitable forming of thebody of the shaped abrasive particle. For example, the first portion 101may have a primary aspect ratio (Lfp:Wfp) of at least about 1:1. Inother embodiments, the first portion 101 may have a primary aspect ratiothat is about 2:1, such as at least about 3:1, at least about 5:1, oreven at least about 10:1. Still, in one non-limiting embodiment, thefirst portion 101 may have a primary aspect ratio of not greater thanabout 1000:1.

Furthermore, the first portion 101 may be formed to have a particularsecondary aspect ratio, such that the body of the shaped abrasiveparticle has a desirable shape. For example, the first portion 101 canhave a secondary aspect ratio (Lfp:Tfp) of at least about 1:1. In otherembodiments, the first portion 101 may have a secondary aspect ratiothat is at least about 2:1, such as at least about 3:1, at least about5:1, or even at least about 10:1. Still, in one non-limiting embodiment,the secondary aspect ratio of the first portion 101 may be not greaterthan about 1000:1.

In yet another embodiment, the first portion 101 may be formed to have aparticular tertiary aspect ratio (Wfp:Tfp) to facilitate suitableforming of the body of the shaped abrasive particle. For example, thefirst portion 101 may have a tertiary aspect ratio (Wfp:Tfp) of at leastabout 1:1. In other instances, the first portion 101 may have a tertiaryaspect ratio of at least about 2:1, such as at least about 3:1, at leastabout 5:1, or even at least about 10:1. In still another non-limitingembodiment, the first portion 101 can have a tertiary aspect ratio ofnot greater than about 1000:1.

The dimensions of the first portion 101 of the body of the shapedabrasive particle may be formed to have a particular value to facilitateformation of the body having suitable shape and dimensions. Any of theforegoing dimensions (e.g., Lfp, Wfp, Tfp) of the first portion 101 canhave an average dimension of not greater than about 2 mm. In otherinstances, the average dimension of any one of the first portion length(Lfp), first portion width (Wfp), or first portion thickness (Tfp) canhave an average dimension of not greater than about 1 mm, such as notgreater than about 900 microns, not greater than about 800 microns, notgreat than about 700 microns, not greater than about 600 microns, notgreater than about 500 microns, not greater than about 400 microns, notgreater than about 300 microns, not greater than about 200 microns, notgreater than about 150 microns, not greater than about 140 microns, notgreater than about 130 microns, not greater than about 120 microns, notgreater than about 110 microns, not greater than about 100 microns, notgreater than about 90 microns, not greater than about 80 microns, notgreater than about 70 microns, not greater than about 60 microns, oreven not greater than about 50 microns. Still, in another non-limitingembodiment, any one of the first portion length (Lfp), the first portionwidth (Wfp), or the first portion thickness (Tfp) can have an averagedimension that is at least about 0.01 microns, such as at least about0.1 microns, or even at least about 1 micron. It will be appreciatedthat any one of the first portion length, first portion width, or firstportion thickness can have an average dimension within a range betweenany of the minimum and maximum values noted above.

In another embodiment, the first portion 101 may be deposited to have aparticular cross-sectional shape. Deposition of the first portion 101with a particular cross-sectional shape can facilitate formation of abody of a shaped abrasive particle having a particular, desirablecross-sectional shape and three-dimensional shape. In accordance with anembodiment, the first portion 101 can have substantially anycontemplated cross-sectional shape. More particularly, the first portion101 can have a cross-sectional shape in a plane defined by the firstportion length (Lfp) and first portion width (Wfp), such as triangular,quadrilateral, rectangular, trapezoidal, pentagonal, hexagonal,heptagonal, octagonal, ellipsoids, a Greek alphabet letter, a Latinalphabet character, a Russian alphabet character, a Kanji character,irregular shaped contours, and any combination thereof. Furthermore, thefirst portion 101 may be formed to have a particular cross-sectionalshape in a plane defined by the first portion length (Lfp) and firstportion thickness (Tfp). Such cross-sectional shape can include a shapeselected from the group of triangular, quadrilateral, rectangular,trapezoidal, pentagonal, hexagonal, heptagonal, octagonal, ellipsoids, aGreek alphabet letter, a Latin alphabet character, a Russian alphabetcharacter, a Kanji character, irregular shaped contours, and anycombination thereof.

In at least one embodiment, the first portion 101 may be deposited inthe form of a layer. In yet another embodiment, the first portion may bedeposited (as shown in FIG. 1A) as an elongated structure, where thelength is significantly greater than the thickness or the width. In yetanother embodiment, the first portion 101 may deposited as a discretedroplet. More particularly, the deposition process may be conducted suchthat it includes depositing a plurality of discrete droplets of apredetermined volume of the first print material 102 to form the firstportion 101. For example, the first portion 101 may be made up of aplurality of first sub-portions that are deposited in a controlledmanner to define the dimensions of the first portion 101.

As further illustrated in FIG. 1A, the process of forming a shapedabrasive particle according to an additive manufacturing process alsocan include controlled deposition of a second portion 110 including asecond print material 112. In an embodiment, the second print material112 can include a solid, a solution, a mixture, a liquid, a slurry, agel, a binder, and a combination thereof. In a particular embodiment,the second print material 112 can be the same as, or different from, thefirst print material. For example, the second print material 112 caninclude a sol gel material as described above. The deposition assembly151 can deposit the second portion 110 in any suitable locationincluding a particular location relative to the first portion 101. Forexample, as illustrated in FIG. 1A, the second portion 110 may bedeposited in a position to abut at least a portion of the first portion101. Such controlled multi-axial movement of the deposition assembly 151can facilitate both precise deposition of discrete portions including,for example, the first portion 101 and the second portion 110, as wellas controlled and precise deposition of a plurality of portions (andsub-portions) with respect to each other, thus facilitating thecompilation of a plurality of portions to form the body of the shapedabrasive particle.

As illustrated, the deposition assembly 151 can be configured to depositthe second print material 112 as the second portion 110 of the body ofthe shaped abrasive particle. In particular, the second portion 110 candefine a fraction of the total volume of the body of the shaped abrasiveparticle. In particular instances, the second portion 110 can have asecond portion length (Lsp), a second portion width (Wsp), and a secondportion thickness (Tsp). Notably, according to one aspect, Lsp can begreater than or equal to Wsp, Lsp can be greater than or equal to Tsp,and Wsp can be greater than or equal to Tsp. In particular instances,the length (Lsp) of the second portion 110 may define the largestdimension of the second portion 110, and the width (Wsp) of the secondportion 110 may define a dimension extending in a direction generallyperpendicular to the length (Lsp) and may define the second largestdimension in accordance with an embodiment. Finally, in someembodiments, the thickness (Tsp) of the second portion 110 may definegenerally the smallest dimension of the second portion 110, and maydefine a dimension extending in a direction perpendicular to either orboth of the length (Lsp) and the width (Wsp). It will be appreciated,however, that the second portion 110 can have various shapes as will bedefined further herein.

In accordance with an embodiment, the second portion 110 can have aprimary aspect ratio (Lsp:Wsp) that can facilitate formation of a bodyhave a suitable shape and dimensions. For example, the second portion110 can have a primary aspect ratio (Lsp:Wsp) of at least about 1:1. Inother embodiments, the second portion 110 may have a primary aspectratio that is about 2:1, such as at least about 3:1, at least about 5:1,or even at least about 10:1. Still, in one non-limiting embodiment, thesecond portion 110 may have a primary aspect ratio of not greater thanabout 1000:1.

Furthermore, the second portion 110 may be formed to have a particularsecondary aspect ratio, such that the formed body of the shaped abrasiveparticle has a desirable shape. For example, the second portion 110 canhave a secondary aspect ratio (Lsp:Tsp) of at least about 1:1. In otherembodiments, the second portion 110 may have a secondary aspect ratiothat is at least about 2:1, such as at least about 3:1, at least about5:1, or even at least about 10:1. Still, in one non-limiting embodiment,the secondary aspect ratio of the second portion 110 may be not greaterthan about 1000:1.

In yet another embodiment, the second portion 110 may be formed to havea particular tertiary aspect ratio (Wsp:Tsp) that can facilitateformation of a body have a suitable shape and dimensions. For example,the second portion 110 can have a tertiary aspect ratio (Wsp:Tsp) of atleast about 1:1. In other instances, the second portion 110 may have atertiary aspect ratio of at least about 2:1, such as at least about 3:1,at least about 5:1, or even at least about 10:1. In still anothernon-limiting embodiment, the second portion 110 can have a tertiaryaspect ratio of not greater than about 1000:1.

The dimensions of the second portion 110 of the body of the shapedabrasive particle may be formed to have a particular value. Any of theforegoing dimensions (e.g., Lsp, Wsp, Tsp) of the second portion 110 canhave an average dimension of not greater than about 2 mm. In otherinstances, the average dimension of any one of the second portion length(Lsp), second portion width (Wsp), or second portion thickness (Tsp) canhave an average dimension of not greater than about 1 mm, such as notgreater than about 900 microns, not greater than about 800 microns, notgreat than about 700 microns, not greater than about 600 microns, notgreater than about 500 microns, not greater than about 400 microns, notgreater than about 300 microns, not greater than about 200 microns, notgreater than about 150 microns, not greater than about 140 microns, notgreater than about 130 microns, not greater than about 120 microns, notgreater than about 110 microns, not greater than about 100 microns, notgreater than about 90 microns, not greater than about 80 microns, notgreater than about 70 microns, not greater than about 60 microns, oreven not greater than about 50 microns. Still, in another non-limitingembodiment, any one of the second portion length (Lsp), the secondportion width (Wsp), or the second portion thickness (Tsp) can have anaverage dimension that is at least about 0.01 microns, such as at leastabout 0.1 microns, or even at least about 1 micron. It will beappreciated that any one of the second portion length, second portionwidth, or second portion thickness can have an average dimension withina range between any of the minimum and maximum values noted above.

In another embodiment, the second portion 110 may be deposited to have aparticular cross-sectional shape. Deposition of the second portion 110with a particular cross-sectional shape can facilitate formation of abody of a shaped abrasive particle having a particular, desirablecross-sectional shape and three-dimensional shape. In accordance with anembodiment, the second portion 110 can have substantially anycontemplated cross-sectional shape. More particularly, the secondportion 110 can have a cross-sectional shape in a plane defined by thesecond portion length (Lsp) and second portion width (Wsp), which may beviewed top-down, where the shape is selected from the group oftriangular, quadrilateral, rectangular, trapezoidal, pentagonal,hexagonal, heptagonal, octagonal, ellipsoids, a Greek alphabet letter, aLatin alphabet character, a Russian alphabet character, a Kanjicharacter, complex polygonal shapes, irregular shaped contours, and anycombination thereof. Furthermore, the second portion 110 may be formedto have a particular cross-sectional shape in a plane defined by thesecond portion length (Lsp) and second portion thickness (Tsp), whichmay be evident in a side-view. Such cross-sectional shape can include ashape selected from the group of triangular, quadrilateral, rectangular,trapezoidal, pentagonal, hexagonal, heptagonal, octagonal, ellipsoids, aGreek alphabet letter, a Latin alphabet character, a Russian alphabetcharacter, a Kanji character, complex polygonal shapes, irregular shapedcontours, and any combination thereof. Moreover, the second portion 110may be formed to have a particular cross-sectional shape in a planedefined by the second portion width (Wsp) and second portion thickness(Tsp), which may be evident in a side-view. Such cross-sectional shapecan include a shape selected from the group of triangular,quadrilateral, rectangular, trapezoidal, pentagonal, hexagonal,heptagonal, octagonal, ellipsoids, a Greek alphabet letter, a Latinalphabet character, a Russian alphabet character, a Kanji character,complex polygonal shapes, irregular shaped contours, and any combinationthereof.

In at least one embodiment, the second portion 110 may be deposited inthe form of a layer. In yet another embodiment, the second portion maybe deposited (as shown in FIG. 1A) as an elongated structure, where thelength is significantly greater than the thickness or the width. In yetanother embodiment, the second portion 110 may be deposited as adiscrete droplet. More particularly, the deposition process may beconducted such that it includes depositing a plurality of discretedroplets of a predetermined volume of the second print material 112 toform the second portion 110. For example, the second portion 110 may bemade up of a plurality of second sub-portions that are deposited in acontrolled manner to define the dimensions of the second portion 110.

As further illustrated in FIG. 1A, the first portion 101 can havesubstantially the same cross-sectional shape as the cross-sectionalshape of the second portion 110. However, it will be appreciated that inother embodiments, a plurality of portions may be deposited such thateach of the portions can have a different cross-sectional shape withrespect to each other. For example, in at least one embodiment, thefirst portion 101 can be deposited with a first cross-sectional shapewith respect to any two dimensions (e.g., length, width, and thickness)of the body of the first portion that can be different than across-sectional shape of the second portion 110 with respect to any twodimensions (e.g., length, width, thickness) defining the body of thesecond portion 110.

In accordance with some embodiments, the first print material 102 canhave a first composition and the second print material 112 can have asecond composition. In some instances, the first composition can besubstantially the same as the second composition. For example, the firstcomposition and second composition can be essentially the same withrespect to each other, such that only a content of impurity materialspresent in small amounts (e.g., such as less than about 0.1%) mayconstitute a difference between the first composition and the secondcomposition. Alternatively, in another embodiment, the first compositionand second composition can be significantly different with respect toeach other.

In at least one embodiment, the first composition can include a materialsuch as an organic material, inorganic material, and a combinationthereof. More particularly, the first composition may include a ceramic,a glass, a metal, a polymer, or any combination thereof. In at least oneembodiment, the first composition may include a material such as anoxide, a carbide, a nitride, a boride, an oxycarbide, an oxynitride, anoxyboride, and any combination thereof. Notably, in one embodiment, thefirst composition can include alumina. More particularly, the firstcomposition may include an alumina-based material, such as a hydratedalumina material including, for example, boehmite.

In at least one embodiment, the second composition can include amaterial such as an organic material, inorganic material, and acombination thereof. More particularly, the second composition mayinclude a ceramic, a glass, a metal, a polymer, or any combinationthereof. In at least one embodiment, the second composition may includea material such as an oxide, a carbide, a nitride, a boride, anoxycarbide, an oxynitride, an oxyboride, and any combination thereof.Notably, in one embodiment, the second composition can include alumina.More particularly, the first composition may include an alumina-basedmaterial, such as a hydrated alumina material including, for example,boehmite.

In certain instances, the process of depositing a first print materialand second print material (e.g., the first print material 110 and thesecond print material 112) can be conducted such that the first printmaterial is deposited at a first time and the second print material isdeposited at a second time and the first time and second time arediscrete in different time intervals. In such embodiments, thedeposition process can be an intermittent process, wherein thedeposition process includes the formation of discrete portions duringdiscrete durations of time. In an intermittent process, at least aportion of time passes between the formation of the first portion andthe formation of the second portion, wherein there may be no depositionof material.

Still, in other instances, it will be appreciated that the depositionprocess may be a continuous process. In continuous processes, thedeposition process may not necessarily include the deposition ofdiscrete first and second portions at different time intervals. Instead,the deposition process may utilize a continuous extrusion process inwhich print material can be extruded while the deposition assembly 151is moving. Moreover, the deposition assembly 151 may be capable ofchanging the dimension of the portion during the continuous depositionprocess, thereby facilitating the formation of one or more portions witha variable dimensions (e.g., cross-sectional and three-dimensionaldimensions) to facilitate the formation of a body of a shaped abrasiveparticle having a desirable two-dimensional and three-dimensional shape.

In accordance with another aspect of forming a body of a shaped abrasiveparticle via an additive manufacturing process, the process can includepreferentially modifying one of the first portion 101 and the secondportion 110 to join the first portion 101 and the second portion 110 andform a subsection 171 of the body. In a particular embodiment, theprocess of modifying can include changing a phase of at least one of thefirst print material 102 and the second print material 112. For example,modifying can include heating at least one of the first portion 101 andthe second portion 110. More particularly, heating can include joining apart of the first portion 101 to the second portion 110, such as byfusing at least a part of the first portion 101 to the second portion110. Heating also may be accomplished utilizing various techniquesincluding, for example, convection, conduction, and radiationtechniques. In one particular embodiment, the process of heating atleast one of the first portion 101 and second portion 110 can includeimpinging electromagnetic radiation on at least a portion of the firstportion 110 and/or second portion 110 to facilitate joining a portion ofthe first portion 101 to the second portion 110. Suitable types ofelectromagnetic radiation may be supplied by use of a laser. Still, itwill be appreciated that in other instances, the process of heating caninclude impinging electromagnetic radiation on at least a portion of thesecond portion to facilitate joining any one of the first portion andsecond portion.

In other instances, the process of modifying a portion of the body alsocan include melting, selective laser melting, sintering, selectivesintering, direct metal laser sintering, selective laser sintering,particle beam modification, electron beam melting, fused depositionmodeling, curing, and any combination thereof. Any of the foregoingprocesses can be used on a part or all of any of one or more of theportions to modify the portions.

In another aspect of forming a body of a shaped abrasive particle via anadditive manufacturing process, the process of forming a body of ashaped abrasive particle can be conducted according to a digital model.The process of forming a body according to a digital model can includemeasuring at least a portion of the body and comparing it to acorresponding dimension of the digital model. The process of comparingcan be conducted during the forming process or after the forming processis completed for a portion or the entire body. It will be appreciatedthat the provision of a digital model can facilitate the control of andthe deposition process conducted by the deposition assembly 151.

In particular instances, the process of forming a body according to adigital model can further include creating a plurality of digitalcross-sections of the digital model. Creation of the plurality ofdigital cross-sections can facilitate, for example, controlleddeposition of one or more portions of the body. For example, in oneinstance, the process can include depositing a first portion of the bodyat a first time, where the first portion corresponds to a firstcross-section of a plurality of cross-sections of the digital model.Furthermore, the process can include depositing a second portion of thebody distinct from the first portion at a second time that is differentthan the first time. The second portion can correspond to a secondcross-section of the plurality of cross-sections of the digital model.Accordingly, it will be appreciated that the plurality of digitalcross-sections can be a guide for depositing the plurality of discreteportions, where a single digital cross-section can facilitate thedeposition of a discrete first portion and a second digitalcross-section can facilitate the deposition of a second discreteportion. Each of the portions may be deposited, and while the depositionassembly 151 is depositing and forming each of the portions, thedimensions of the portions can be measured and compared to a digitalmodel. More particularly, the deposition assembly 151 may be adapted toalter the deposition process based on the comparison of the dimensionsof the deposited portion to a corresponding digital model portion.

It also will be appreciated that an additive manufacturing process caninclude a process of compiling discrete portions including, for example,the first portion 101 and second portion 110, to form a subsection 171.Furthermore, the process may include compiling a plurality ofsubsections to form the body of the shaped abrasive particle.

In accordance with yet another embodiment, the process of forming theshaped abrasive particle can include a subtractive process. Notably, thesubtractive process may be conducted after completing at least some ofthe additive manufacturing process. More particularly, the subtractiveprocess may be conducted after total completion of the additivemanufacturing process. In at least one embodiment, the subtractiveprocess can be conducted after forming a body of a precursor shapedabrasive particle. In certain instances, the subtractive process caninclude removing at least a portion of the material used to form theprecursor shaped abrasive particle. Certain suitable subtractiveprocesses may include, for example, forming at least one opening withina portion of the body, forming at least one aperture that extendsthrough an entire portion of the body, and heating the body to remove aportion of the body, such as by volatilizing at least a portion of thebody.

The body of a shaped abrasive particle that has been formed by anadditive manufacturing process can include a variety of suitabledimensions. In particular instances, the body can have a body length(Lb), a body width (Wb), and a body thickness (Tb), such as shown inFIG. 6. In one non-limiting embodiment, the length of the body maydefine the largest dimension of the shaped abrasive particle and thewidth of the body may define a dimension extending in a directiongenerally perpendicular to the length and may define the second largestdimension in accordance with an embodiment. Moreover, in someembodiments, the thickness of the body may define the smallest dimensionof the shaped abrasive particle, and may define a dimension extending ina direction perpendicular to either or both of the length and the width.In some instances, Lb may be greater than or equal to Wb, and Lb may begreater than or equal to Tb. Yet, in other designs of the shapedabrasive particles, Wb may be greater than or equal to Tb. It will beappreciated, however, that the body can have various shapes as will bedefined further herein.

Moreover, reference herein to any dimensional characteristic (e.g., Lb,Wb, Tb) can be reference to a dimension of a single shaped abrasiveparticle of a batch, a median value, or an average value derived fromanalysis of a suitable sampling of shaped abrasive particles from abatch. Unless stated explicitly, reference herein to a dimensionalcharacteristic can be considered reference to a median value that is abased on a statistically significant value derived from a sample size ofa suitable number of articles from a batch of articles. Notably, forcertain embodiments herein, the sample size can include at least 10randomly selected articles from a batch of articles. A batch of articlesmay be a group of articles that are collected from a single process run.Additionally or alternatively, a batch of articles may include an amountof shaped abrasive particles suitable for forming a commercial gradeabrasive product, such as at least about 20 lbs. of particles.

In accordance with an embodiment, the body can have a primary aspectratio (Lb:Wb) of at least about 1:1. In other embodiments, the body mayhave a primary aspect ratio that is about 2:1, such as at least about3:1, at least about 5:1, or even at least about 10:1. Still, in onenon-limiting embodiment, the body may have a primary aspect ratio of notgreater than about 1000:1.

Furthermore, the body may be formed to have a particular secondaryaspect ratio, such that the shaped abrasive particle has a desirableshape. For example, the body can have a secondary aspect ratio (Lb:Tb)of at least about 1:1. In other embodiments, the body may have asecondary aspect ratio that is at least about 2:1, such as at leastabout 3:1, at least about 5:1, or even at least about 10:1. Still, inone non-limiting embodiment, the secondary aspect ratio of the body maybe not greater than about 1000:1.

In yet another embodiment, the body may be formed to have a particulartertiary aspect ratio (Wb:Tb) of at least about 1:1. In other instances,the body may have a tertiary aspect ratio of at least about 2:1, such asat least about 3:1, at least about 5:1, or even at least about 10:1. Instill another non-limiting embodiment, the body can have a tertiaryaspect ratio of not greater than about 1000:1.

The dimensions of the body of the shaped abrasive particle may be formedto have a particular value. Any of the foregoing dimensions (e.g., Lb,Wb, Tb) of the body can have an average dimension of at least about 0.1microns. In other instances, the average dimension of any one of thebody length (Lb), body width (Wb), or body thickness (Tb) can have anaverage dimension of at least about 1 micron, at least about 10 microns,at least about 50 microns, at least about 100 microns, at least about150 microns, at least about 200 microns, at least about 400 microns, atleast about 600 microns, at least about 800 microns, at least about 1mm. Still, in another non-limiting embodiment, any one of the bodylength (Lb), the body width (Wb), or the body thickness (Tb) can have anaverage dimension that is not greater than about 20 mm, not greater thanabout 18 mm, not greater than about 16 mm, not greater than about 14 mm,not greater than about 12 mm, not greater than about 10 mm, not greaterthan about 8 mm, not greater than about 6 mm, or even not greater thanabout 4 mm. It will be appreciated that any one of the dimensions canhave an average dimension within a range between any of the minimum andmaximum values noted above.

In another embodiment, the body may be formed to have a particular,desirable cross-sectional shape. For example, the body can have across-sectional shape in a plane defined by the body length (Lb) andbody width (Wb), where the shape is selected from the group oftriangular, quadrilateral, rectangular, trapezoidal, pentagonal,hexagonal, heptagonal, octagonal, ellipsoids, a Greek alphabet letter, aLatin alphabet character, a Russian alphabet character, a Kanjicharacter, complex polygonal shapes, irregular shaped contours, and anycombination thereof. Furthermore, the body may be formed to have aparticular cross-sectional shape in a plane defined by the body length(Lb) and the body thickness (Tb). Such cross-sectional shape also caninclude a shape selected from the group of triangular, quadrilateral,rectangular, trapezoidal, pentagonal, hexagonal, heptagonal, octagonal,ellipsoids, a Greek alphabet letter, a Latin alphabet character, aRussian alphabet character, a Kanji character, complex polygonal shapes,irregular shaped contours, and any combination thereof.

The body also may be formed to have a particular, desirablethree-dimensional shape. For example, the body can have athree-dimensional shape selected from the group consisting of apolyhedron, a pyramid, an ellipsoid, a sphere, a prism, a cylinder, acone, a tetrahedron, a cube, a cuboid, a rhombohedrun, a truncatedpyramid, a truncated ellipsoid, a truncated sphere, a truncated cone, apentahedron, a hexahedron, a heptahedron, an octahedron, a nonahedron, adecahedron, a Greek alphabet letter, a Latin alphabet character, aRussian alphabet character, a Kanji character, complex polygonal shapes,irregular shaped contours, a volcano shape, a monostatic shape, and acombination thereof. A monostatic shape is a shape with a single stableresting position. Accordingly, shaped abrasive particles having amonostatic shape can be applied to a substrate and consistently beoriented in the same position, as they have only one stable restingposition. For example, shaped abrasive particles having a monostaicshape may be suitable when applying the particles to a backing viagravity coating, which may be used in the formation of a coated abrasiveproduct. More particularly, the shaped abrasive particles may bemono-monostatic shapes, which describe three dimensional objects havinga shape with only one unstable point of balance. According to oneparticular embodiment, the shaped abrasive particle may have the shapeof a gömböc. In another embodiment, the shaped abrasive particle is amonostatic polyhedron with at least four surfaces.

The additive manufacturing process according to the embodiments hereinalso may be used to form a plurality of shaped abrasive particles, whereeach of the shaped abrasive particles of the plurality of shapedabrasive particles have a body having a body length (Lb) a body width(Wb), and a body thickness (Tb) as described above. In accordance withan embodiment, the plurality of shaped abrasive particles can have atleast one of a body length variation of not greater than about 50%, abody width variation of not greater than about 50%, and a body thicknessvariation of not greater than about 50%.

The body length variation may be described as a standard deviation ofbody length for a suitable sampling from a plurality of shaped abrasiveparticles, which can include a plurality of shaped abrasive particles.In an embodiment, the body length variation may be not greater thanabout 40%, such as not greater than about 30%, not greater than about20%, not greater than about 10%, or even not greater than about 5%.

Like the body length variation, the body width variation may be ameasure of the standard deviation of the width of the body for asuitable sampling of shaped abrasive particles from the plurality ofshaped abrasive particles. In accordance with an embodiment, the bodywidth variation may be not greater than about 40%, such as not greaterthan about 30%, and not greater than about 20%, not greater than about10%, or even not greater than about 5%.

Furthermore, the body thickness variation may be a standard deviation ofbody thickness for a suitable sampling of shaped abrasive particles fromthe plurality of shaped abrasive particles. In accordance with oneembodiment, the body thickness variation for the plurality of shapedabrasive particles may be not greater than about 40%, such as notgreater than about 30%, not greater than about 20%, not greater thanabout 10%, or even not greater than about 5%.

In accordance with an embodiment the additive manufacturing process caninclude forming a body of a shaped abrasive particle by shaping a rawmaterial without the use of a production tool. It will be appreciatedthat a production tool may refer to a mold or screen having one or moreopenings configured to contain and form the raw material into thedesired final shaped abrasive particle. In accordance with anotherembodiment, the additive manufacturing process can include forming abody of a shaped abrasive particle by depositing a plurality of discreteportions of raw material in a controlled, non-random manner relative toeach other. Still, in at least one embodiment, the additivemanufacturing process can include depositing a plurality of portions ofthe body in a controlled, non-random manner relative to each other intoa production tool. That is, in certain instances the additivemanufacturing process can include use of a production tool. In at leastone manner, the additive manufacturing process is distinct fromconventional screen printing and molding processes as the productiontool can be filled with a plurality of discrete portions that are placedinto the production tool in a controlled-nonrandom manner.

Reference herein to formation of a shape abrasive particle will beunderstood to include formation of a precursor shaped abrasive particle.That is the additive manufacturing process may form a precursor shapedabrasive particle, which may be a green body or unfinished body that canundergo further processing to form the final shaped abrasive particle.In certain forming processes, the precursor shaped abrasive particle mayhave essentially the same shape of the final shaped abrasive particle.

In accordance with another embodiment, the additive manufacturingprocess can include processes such as light photopolymerization, laserpowder forming, powder bed fusion, selective laser centering,micro-laser sintering, material extrusion, robocasting, materialjetting, sheet lamination, and a combination thereof. In one particularembodiment, the light photopolymerization process can includestereolithography. Stereolithography can include a process wherein atleast one layer of a slurry containing a polymer material can bepolymerized during the forming process to form a shaped abrasiveparticle. More particularly, the stereolithography process can includeprovision of a mixture, such as a slurry containing a powder rawmaterial and a carrier, and a polymer material that is configured to bepolymerized during the forming process of forming the shaped abrasiveparticle.

In another embodiment the additive manufacturing process can include alaser powder forming process. Laser powder forming can includedeposition of a raw material on a target, such as substrate and animpinging radiation, such as from a laser source, at the target and rawmaterial to melt the raw material and form the raw material into atleast a portion of a shaped abrasive particle. Notably, the laser powderforming process can include a change of phase of the raw material from asolid state to a liquid state such that a melt is formed prior toformation of at least a portion of the shaped abrasive particle.

The laser powder forming process can utilize a raw material selectedfrom the group of materials such as a metal, a metal alloy, a glass, aceramic, a polymer, and a combination thereof. In at least oneparticular embodiment, the shaped abrasive particle formed by the laserpowder forming process can include a material such as a metal, a metalalloy, a glass, a ceramic, a ceramic precursor, a polymer, and acombination thereof. The shaped abrasive particles in one embodimentformed by a laser powder forming process can consist essentially of aglass material comprising oxide.

In another instance, the additive manufacturing process can include aselective laser sintering process. Selective laser sintering can includea process wherein radiation is directed to a target. The radiation maybe supplied from a laser source. The radiation can be impinged on atarget that includes a raw material, and the radiation can change atleast a portion of the raw material into a portion of a shaped abrasiveparticle. In more particular instances, the selective laser sinteringprocess can include impinging radiation from a laser source onto aportion of a bed of raw material and converting a portion of the bed ofraw material into a shaped abrasive particle. For example, a portion ofthe bed of raw material impinged by the radiation can be converted in amanner such that it may undergo a phase change, while other portions ofthe raw material not subject to the radiation may maintain theiroriginal state. In accordance with an embodiment, changing at least aportion of the raw material can include a change in a crystallinestructure of the raw material. For example, the bed of raw material mayinclude a boehmite material that is changed by the radiation into analternative form of alumina, including for example, alpha alumina. Inyet another embodiment, changing at least a portion of the raw materialcan include changing a phases of the raw material, such as changing theraw material subject to the radiation from a solid phase to a liquidphase.

The raw material used in the selective laser sintering operation caninclude a metal, a metal alloy, a glass, a ceramic, a ceramic precursor,a polymer, and a combination thereof. In one particular embodiment, theraw material can include an oxide material, such as alumina or boehmite.Moreover, the shaped abrasive particle formed by the selective lasersintering process can include a metal, a metal alloy, a glass, aceramic, a ceramic precursor, a polymer, and a combination thereof. Inone particular embodiment, the shaped abrasive particle formed accordingto the selective laser sintering process can include an oxide material,such as alumina or boehmite.

And yet another embodiment the additive manufacturing process caninclude material jetting. A material jetting process can includedeposition of discrete droplets of raw material onto a target andcoalescence of the discrete droplets into at least a portion of the bodyof the shape abrasive particle.

According to one alternative process, the shaped abrasive particles canbe formed using a low pressure injection molding process. Unlike certainconventional injection molding processes, a molding material, which caninclude any of the properties of the print material of the embodimentsherein directed to an additive manufacturing process, can be injectedinto a mold in a controlled manner. In particular, during the process,the mold material can be injected into the mold under laminar flowconditions as opposed to turbulent flow conditions. The laminar flowconditions allow for controlled placement of the mold material into themold according to a filling procedure, which may include selectiveplacement of the mold material into portions of the mold in a particularsequence for a controlled filling procedure. The injection moldingprocess may be combined with one or more processes described herein.

In accordance with one particular embodiment, the additive manufacturingprocess for forming the shaped abrasive particle can includerobocasting. In certain instances, robocasting can include thedeposition of a raw material onto a target in the form of discreteportions that are distinct from each other. The portions may be latercoalesced through subsequent processing to form the shape abrasiveparticles. The raw material may be deposited from a nozzle onto a targetor substrate in a controlled manner to form the body of the shapedabrasive particle.

In accordance with an embodiment, the process of forming the body viarobocasting can include controlling at least one process parameter fromthe group consisting of a nozzle tip length; a nozzle width; a nozzleaspect ratio, a deposition pressure, a relationship between nozzle widthand deposition pressure, a deposition rate, a deposition volume, arelationship between deposition rate and deposition position, arelationship between deposition pressure and deposition position, ashutoff distance, premove delay, a dispense gap, a filling pattern ofthe print material, a dynamic yield stress (σd) of a print material, astatic yield stress (σs) of a print material, a yield stress ratio(σd/σs) of a print material, and a combination thereof.

In particular instances, the process of forming the body can includedeposition or depositing a first print material as the first portportion of the body the first time and depositing a second printmaterial as a second portion of the body distinct from the first portionand the second time. FIG. 1B includes an illustration of a portion of asystem and method of forming a shaped abrasive particle according to anembodiment. As illustrated, the first deposition assembly 151 can beconfigured to deposit a first print material 122 and form at least thefirst portion 141 or the second portion 142. Certain processes mayutilize a second deposition assembly 143 configured to deposit a secondprint material 147 from a second deposition head (i.e., second nozzle)144 onto a target to form the first portion 141 or the second portion142. In accordance with an embodiment, depositing the first material 122can include forming the first portion 141 (e.g., in the form of a layer)at a first time and depositing the second print material 147 as thesecond portion 142 (e.g., in the form of a layer) overlying the firstportion 141.

In accordance with one embodiment, the first portion 141 can have afirst characteristic selected from the group of hardness, porosity,composition, and a combination thereof. Moreover, in another embodiment,the second portion 142 can have a second characteristic selected fromthe group of hardness, porosity, composition, and a combination thereof.In at least one embodiment, the first characteristic can be differentfrom the second characteristic.

In certain instances, the first print material 122 can have a firstcomposition and the second print material 147 can have a secondcomposition. The first composition and second composition can besignificantly different compared to each other. For example, the firstand second compositions can differ from each other in terms of primarycompositional species, which are distinct from trace amount species thatare otherwise undetectable. In particular instances, the first andsecond compositions can be different from each other based on adifference of at least 2% of one of the primary compositional species inthe first and second compositions.

In another embodiment, the second composition can have a differentporosity relative to the porosity of the first composition. For example,in one embodiment, the first portion 141 may have a first porosity thatis different than a second porosity of the second portion 142. Moreparticularly, the first portion can have a first porosity that isgreater than the second porosity of the second portion 142. According toat least one embodiment, the body can be formed to have selectiveporosity in particular portions, which may be suitable to facilitatecertain the mechanical properties and abrasive capabilities of theshaped abrasive particle. In certain instances, the body can be formedwith one or more portions (e.g., layers) having a select porosity tocontrol the fracture mechanics of the shape abrasive particle.

Any another embodiment, the first print material 122 and the secondprint material 137 can be deposited in different regions within thebody. For example, referring to FIG. 1, the first portion 141 caninclude the first print material 122 and the second portion 142 caninclude the second print material 147. Controlled deposition of thefirst print material 122 and second print material 137 may be suitableto control the mechanical properties and abrasive characteristics of theshaped abrasive particle. For example, controlled deposition of thefirst print material 122 and second print material 137 may be suitableto form a shaped abrasive particle having a controlled fracturingbehavior. For example, the first print material 122 can have a firstcomposition and the second print material 147 can have a secondcomposition, and the forming process can include selective deposition ofthe first and second compositions with respect to each other within thebody to affect the fracturing behavior of the shaped abrasive particles.For example, in one particular embodiment, the first print material 122and the second print material 147 can be deposited in alternative layerswith respect to each other within a region of the body to form acomposite body, which may configured to control a self-sharpeningbehavior of the body.

In another embodiment, the first portion 141 can have a first hardnessthat is distinct from a second hardness associated with the secondportion 142. For example: one embodiment, the first portion 141 and thesecond portion 142 can have a difference in hardness relative to eachother. In certain instances, the first hardness of the first portion 141can be greater than the second hardness of the second portion 142. Inone particular instance, the first portion 141 and second portion 42 canbe deposited in a particular arrangement relative to each other, whichmay facilitate improved fracturing behavior and performance of theshaped abrasive particle.

In yet another embodiment, the first print material 122 and second printmaterial 147 can be deposited in different regions of the body to form acomposite body including a controlled arrangement of the regionsrelative to an intended orientation of the shaped abrasive particle in afixed abrasive article. For example, the first print material 122 andsecond print material 147 can be arranged within the body such that whenthe shaped abrasive particle is deployed within a fixed abrasive article(e.g., bonded abrasive, coated abrasive, nonwoven abrasive, etc.) thefirst print material 122 and the second print material 147 are arrangedrelative to the intended orientation of the particle in the fixedabrasive. Control of the orientation of the first print material 122 andthe second print material 147 within the body of the shaped abrasiveparticle and relative to the intended orientation of the body in thefixed abrasive may facilitate improved performance of the shapedabrasive particle and the fixed abrasive article.

In certain instances, the forming process can include depositing thefirst portion 141 having a first volume that is different than a secondvolume associated with the second portion 142. For example, asillustrated in FIG. 1B, the first portion 141 can have a first volumethat is different than a volume of the second portion 142. Moreparticularly, in certain instances, the first portion 141 can have afirst volume that can be greater than the second volume of the secondportion 142. According to one particular embodiment, the volume of theportions can decrease as the forming process continues, such that thevolume of portions formed subsequent to the initial portion decreasesrelative to the volume of the initial portion.

In accordance with an embodiment, the process of controlled depositionof the first portion and second portion may be suitable to control thesize of certain features of the body of the shaped abrasive particle.For example, in at least one embodiment, the first portion 141 can havea first volume that is greater than a second volume of the secondportion 142. In such instances, the first portion 141 may define acentral region of the body and the second portion 142 may define atleast a portion of a corner of the body. More particularly, the firstportion 141 may define a central region of the body and the secondportion 142 may define an edge of the body. Notably, it will beappreciated that for certain shaped abrasive particles, it may bedesirable to form certain portions of the body using smaller portions,such as the edges and the corners, such that these portions of the bodyhave smaller features and can act as sharp edges or sharp corners.Accordingly, the forming process can include controlled volumedeposition at certain portions of the body to facilitate control of theshape and size of certain features, which may facilitate improvedperformance of the shaped abrasive particle.

As further illustrated in FIG. 1B, the process of forming can includeutilization of a first deposition assembly 151, a first deposition head153, and a first print material 122, that may be deposited from thefirst deposition assembly 151. As noted in the embodiments herein, theutilization of a second deposition assembly 143 may facilitate theselective deposition of a second print material 147, which may bedistinct in various manners from the first print material 122 associatedwith the first deposition assembly 151. For example, in at least oneembodiment, the first portion 141 may be formed by one of the firstdeposition assembly 151 or the second deposition assembly 143. Asdescribed in embodiments herein, the process of forming the body caninclude depositing at least a first print material 122, from the firstdeposition head 153 (i.e., nozzle 153) onto a target, wherein themovement of the nozzle may be controlled by a computer program.

As will be appreciated, in certain forming processes, such as theforming process illustrated in FIGS. 1A and 1B, the process of formingcan include controlling a three-dimensional movement of the nozzleconfigured for deposition of a print material relative to a target. Incertain instances, controlling three-dimensional movement can includecontrol of the nozzle in an X-axis, Y-axis, the Z-axis. Furthermore, asillustrated in FIG. 1B, the process may utilize a plurality of nozzles,wherein each nozzle of the plurality of nozzles can be configured todeposit a print material. The process can include control of each of thenozzle the plurality of nozzles and a three-dimensional movement, suchas control of the nozzles in an X-axis, Y-axis, and the Z-axis.

In particular instances, the process of forming a body of the shapedabrasive particle having the features described herein may befacilitated by utilization of a nozzle 153 having a particular width162. For example, the nozzle 153 can have a width 162 that may be notgreater than about 200 microns, such as not greater than about 150microns, not greater than about 120 microns, not greater than about 100microns, not greater than about 90 microns, not greater than about 85microns, not greater than about 80 microns, not greater than about 75microns, not greater than about 70 microns, not greater than about 65microns, not greater than about 60 microns, not greater than about 55microns, not greater than about 50 microns, not greater than about 45microns, not greater than about 40 microns, not greater than about 35microns, not greater than about 30 microns, not greater than about 25microns, not greater than about 20 microns. Still, in at least onenon-limiting embodiment, the nozzle 153 may have a width 162 of at leastabout 0.1 microns, such as at least about 1 microns, or even at leastabout 10 microns. It will be appreciated that the nozzle 153 can have awidth 162 within a range between any of the minimum and maximum valuesnoted above, including for example, within a range between at leastabout 0.1 microns and not greater than about 500 microns, such as withina range between at least about 0.1 microns and not greater than about100 microns, or even within a range between at least about 0.1 micronsand not greater than about 80 microns.

It will be appreciated that reference herein to a nozzle width 162 caninclude reference to an interior opening within the nozzle 153. Forexample, referring briefly to FIG. 1E, an illustration of an end of anozzle according to an embodiment is provided. As illustrated, thenozzle 153 can have an opening 155 defining a passage through which theprint material can flow and be deposited. The opening 155 can havevarious two-dimensional shapes, including for example polygon andellipsoidal. In accordance with one embodiment as illustrated in FIG.1E, the opening 155 can have a circular two-dimensional shape, and thusthe diameter 156 defines the width. As such, reference herein to thewidth of the nozzle 153, will be understood to be reference to the widthor diameter of the opening 155 depending upon the two-dimensional shapeof the opening 155.

In yet another embodiment, the nozzle 153 can have a tip length 161defining a longest dimension of the nozzle 153. Control of the tiplength 161 of the nozzle 153 may facilitate improved deposition of theprint material, and ultimately formation of features of the body of theshaped abrasive particle. In accordance with an embodiment, the nozzlecan have a tip length 161 of not greater than about 10 mm, such notgreater than about 8 mm, not greater than about 6 mm, not greater thanabout 5 mm, or even not greater than about 4 mm. Still, and anothernon-limiting embodiment, the nozzle 153 can have a tip length 161 of atleast about 0.1 mm, such as at least about 0.2 mm, at least about 0.5mm, or even at least about 1 mm. It will be appreciated that the tiplength 161 of the nozzle 153 can be within a range between any of theminimum maximum values noted above, including for example, a tip length161 of at least about 0.1 mm and not greater than about 10 mm, such asat least about 0.1 mm and not greater than about 5 mm, or even at leastabout 0.2 mm and not greater than about 4 mm.

In accordance with one embodiment, the nozzle aspect ratio value(width/tip length) of the nozzle 153 may be controlled to facilitateimproved deposition and formation of features of the body of the shapedabrasive particles. For example, the nozzle 153 can have a nozzle aspectratio value (width/tip length) of not greater than about 0.8, such asnot greater than about 0.6, not greater than about 0.5, or even notgreater than about 0.4. Still, and another non-limiting embodiment, thenozzle 153 may have a nozzle aspect ratio value of at least about 0.001,such as at least about 0.005, or even at least about 0.008. It will beappreciated that the nozzle 153 can have a nozzle aspect ratio valuewithin a range between any of the minimum and maximum values notedabove, including for example, at least about 0.001 and not greater thanabout 0.8, such as at least about 0.005 and not greater than about 0.5,or even at least about 0.008 and not greater than about 0.4. It willalso be appreciated that the second deposition head (i.e., second nozzle144) associated with the second deposition assembly 143 can have any ofthe features described in accordance with the first deposition assembly151.

In accordance with an embodiment, the process of forming can includecontrolling a deposition pressure to facilitate suitable deposition ofthe first print material and facilitating formation of a body havingsuitable features for use as a shaped abrasive particle. For example, inat least one embodiment, the deposition pressure can be not greater thanabout greater than about 5 MPa, such as not greater than about 4.5 MPa,not greater than about 4 MPa, not greater than about 3.5 MPa, notgreater than about 3 MPa, not greater than about 2.5 MPa, not greaterthan about 2 MPa, not greater than about 1.8 MPa, not greater than about1.5 MPa, not greater than about 1.3 MPa, not greater than about 1 MPa,not greater than about 0.9 MPa, not greater than about 0.8 MPa, or evennot greater than about 0.7 MPa. Still, in at least one non-limitingembodiment, the deposition pressure can be at least about 0.005 MPa,such as at least about 0.01 MPa, at least about 0.05 MPa, at least about0.08 MPa, or even at least about 0.1 MPa. It will be appreciated thatthe deposition pressure may be within a range between any of the minimumand maximum values noted above, including for example a depositionpressure or at least about 0.05 MPa and not greater than about 5 MPa,such as at least about 0.01 MPa and not greater than about 2 MPa, oreven at least about 0.05 MPa and not greater than about 1.5 MPa.

In certain instances, the process of forming the body can include caninclude controlling the relationship between the nozzle width 162 andthe deposition pressure to define a first forming factor(width/deposition pressure) having a value of at least about 0.2microns/MPa, such as at least about 1 micron/MPa, at least about 2microns/MPa, at least about 4 microns/MPa, at least about 6 microns/MPa,at least about 8 microns/MPa, at least about 10 microns/MPa, at leastabout 12 microns/MPa, at least about 14 microns/MPa, or even at leastabout 16 microns/MPa. Still, in at least one non-limiting embodiment,the first forming factor can have a value of not greater than about1×10⁵ microns/MPa, such as not greater than about 1×10⁴ microns/MPa, notgreater than about 8000 microns/MPa, not greater than about 6000microns/MPa, not greater than about 5000 microns/MPa, not greater thanabout 4000 microns/MPa, not greater than about 3000 microns/MPa, notgreater than about 2000 microns/MPa, not greater than about 1000microns/MPa, not greater than about 500 microns/MPa, not greater thanabout 200 microns/MPa, or even not greater than about 100 microns/MPa.It will be appreciated that the first forming factor can be within arange between any of the minimum and maximum values noted above,including for example, at least about at least about 0.2 microns/MPa andnot greater than about 1×10⁵ microns/MPa—such as at least about 1micron/MPa and not greater than about 6000 microns/MPa, or even at leastabout 2 microns/MPa and not greater than about 1000 microns/MPa.

In yet another embodiment, the process of forming the body can includecontrol of the deposition rate that defines the rate at which the nozzleis moved. Suitable control the deposition rate can facilitate suitableformation of the features of the shaped abrasive particles according tothe embodiments herein. For example, the forming process can includemoving the nozzle a particular deposition rate, such as at least about0.01 mm/s, at least about 0.05 mm/s, at least about 0.08 mm/s, at leastabout 0.1 mm/s, at least about 0.3 mm/s, at least about 0.5 mm/s, atleast about 0.8 mm/s, at least about 1 mm/s, at least about 1.5 mm/s, atleast about 2 mm/s, at least about 2.5 mm/s, at least about 3 mm/s.Still, in another non-limiting embodiment, the process of forming caninclude moving the nozzle at a deposition rate of not greater about 50mm/s, such as not great about 30 mm/s, or even not greater than about 20mm/s. It will be appreciated that the process of forming can include adeposition rate within a range between any of the minimum and maximumvalues noted above, including for example a deposition rate of at leastabout 0.01 mm/s and not greater than about 50 mm/s, such as at leastabout 0.1 mm/s and not greater than about 30 mm/s, or even at leastabout 1 mm/s and not greater than about 20 mm/s.

In accordance with a particular embodiment, the process of forming caninclude controlling a deposition volume of one or more print materialsto form particular portions of the body of the shaped abrasive particle.For example, the process of forming can include controlling thedeposition volume by changing the deposition volume of the printmaterial, depending upon a portion of the body being formed. In at leastone embodiment, the forming process can include depositing a smallervolume of material in a region defining a corner of the body as comparedto the volume of material deposited in the region defining a majorsurface of the body. Such deposition procedures may be particularlysuitable in the formation of sharp edges or corners which may beparticularly suitable for the shaped abrasive particles of theembodiments herein.

The process of depositing controlled volumes can include controllingdeposition volume by controlling at least one of a deposition pressureand the deposition rate of the nozzle. Particularly, the process ofcontrolling deposition volume can include controlling a width, length,and height of the portion (e.g., the first portion 141) of the bodyformed at a first time. Moreover, controlling the deposition volume canfurther include controlling the width of the deposition nozzle used toform the particular portion. For example, a nozzle having a smallerwidth may be used to deposit the print material associated with certainportions of the body (e.g., corners or edges) while a nozzle having agreater nozzle width may be used to deposit a print material associatedwith other portions, such as the major faces or interior portions of thebody.

In still another instance, the process of forming can includecontrolling the relationship between the deposition rate and thedeposition position. In one embodiment, controlling the relationshipbetween deposition rate and deposition position can include changing thedeposition rate depending upon the deposition position. Moreparticularly, controlling the relationship between deposition rate anddeposition position can include varying the deposition rate to changethe size of features in the body. For example, in one embodiment,controlling the relationship between deposition rate and depositionposition can include decreasing the deposition rate at a depositionposition associated with the corner or edge of the body of the shapedabrasive particle relative to a deposition rate associated with adeposition position at a major surface or an interior portion of thebody.

In yet another embodiment, the process of forming can includecontrolling the relationship between deposition pressure and depositionposition. In at least one embodiment, the process of controlling therelationship between deposition pressure and the deposition position caninclude changing the deposition pressure depending upon the depositionposition. In another embodiment, the process of controlling therelationship between the deposition pressure and deposition position caninclude varying the deposition pressure depending on the depositionpressure to change the features in the body. Particularly, in certaininstances, the process of controlling the relationship between thedeposition pressure and deposition position can include decreasing thedeposition pressure at a deposition position associated with a corner oredge of the body of the shaped abrasive particle relative to adeposition pressure associated with a deposition position at a majorsurface or interior portion of the body.

In still another embodiment, the process of forming the body can includecontrolling a premove delay between the initial deposition of the printmaterial from the deposition assembly and the movement of the depositionassembly, including for example, movement of the nozzle from which theprint material can be deposited. For example, the premove delay mayfacilitate suitable formation of the features of the shaped abrasiveparticle, including those that may utilize certain deposition patterns,such as an outside-in and in-side out filling process. The delay betweenthe initiation of the deposition process and the movement of thedeposition assembly can facilitate ensuring that the In at least oneembodiment, the process of forming the body can include utilizing apremove delay greater than about 0 seconds, such as at least about 0.1seconds, or even at least about 0.5 seconds. In still anotherembodiment, the premove delay may be not greater than about 10 seconds,such as not greater about 8 seconds, not greater than about 6 seconds,or even not greater than about 4 seconds. It will be appreciated thatthe premove delay may be within a range between any of the minimummaximum values noted above, including for example, at least about 0.1seconds and not greater than about 10 second, at least about 0.5 secondsand not greater than about 6 seconds.

For at least one embodiment, the process of forming the body can includecontrolling a shut off distance defining a distance the depositionassembly travels between the time at which pressure is no longer appliedto the print material and the print material stops depositing from thedeposition assembly. Control of the shutoff distance can facilitateformation of the features of the shaped abrasive particles of theembodiments herein. The shutoff distance can be less than a dispensegap. In other instances, the shutoff distance can be greater than thedispense gap. According to another embodiment, the shutoff distance canbe substantially the same as the dispense gap, such that the value ofthe dispense gape and the value of the shutoff distance do not vary fromeach other by more than 5%. In certain instances, the shutoff distancecan be not greater than about 2 mm, not greater than about 1 mm, notgreater than about 0.5 mm, not greater than about 0.2 mm, or even notgreater than about 0.1 mm. In at least one non-limiting embodiment, theshutoff distance can be at least about 0.001 mm. It will be appreciatedthat the shutoff distance may be within a range between any of theminimum maximum values noted above, including for example, at leastabout 0.001 mm and not greater than about 1 mm, at least about 0.001 mmand not greater than about 0.2 mm.

The process of forming the body of the shaped abrasive particle canfurther include controlling a dispense gap 163. The dispense gap 163 maydefine a distance between the end of the nozzle 153 and a target 125,which may be a surface of a substrate or surface of another portion ofwhere the print material is intended to be deposited. It has been notedthat control of the dispense gap 163 can facilitate suitable formationof a shaped abrasive particle. In accordance with an embodiment, thedispense gap 163 can have a particular relationship relative to thewidth 162 of the nozzle 153. For example, the dispense gap 163 can benot greater than about 10 W, wherein “W” represents the width 162 of thenozzle 153. In another embodiment, the dispense gap 163 can be notgreater than about 9 W, such as not greater than about 8 W, not greaterthan about 7 W, not greater than about 6 W, not greater than about 5 W,not greater than about 4 W, not greater than about 3 W, not greater thanabout 2 W, or even not greater than about 1 W. Still, and another inembodiment, the dispense gap 163 can be at least about 0.001 W, such asat least about 0.005 W, we least about 0.01 W, or even at least about0.1 W. It will be appreciated that the dispense gap 163 can have a valuewithin a range between any of the minimum and maximum values notedabove, including for example, at least we spoke 0.001 W and not greaterthan about 10 W, at least about 0.05 W and not greater than about 5 W,or even at least about 0.01 W and not greater than about 2 W. It will beappreciated that the second deposition assembly 143 and nozzle 144 canbe controlled such that the dispense gap associated with the use of thenozzle 144 can have the same features as noted above.

In accordance with another embodiment, the dispense gap 163 may have aparticular relationship relative to the thickness “t”, wherein “t”represents the average thickness of the portion of the body formed bythe print material using the nozzle. For example, the dispense gap 163associated with the nozzle 153 can be controlled relative to the averagethickness “t” of the second portion 142 as formed by the nozzle 153. Inaccordance with an embodiment, the dispense gap 163 can be not greaterabout 10t, such as not greater than about 9t, not greater about 8t, notgreater than about 7t, not greater than about 6t, not greater than about5t, not greater than about 4t, not greater than about 3t, not greaterthan about 2t, or even not greater than about 1t. Still, and anothernon-limiting embodiment, the dispense gap 163 can be at least about0.001t, such as at least about 0.05t, or even at least about 0.01t. Itwill be appreciated that the dispense gap 163 can have a value within arange between any of the minimum and maximum values noted above,including for example, at least about 0.001t and not greater than about10t, such as at least about 0.05t and not greater than about 5t, or evenat least about 0.01t and not greater than about 2t.

In at least one embodiment, the process of forming the body can includecontrolling the dispense gap 163 by varying the dispense gap 163 suchthat the first print material 122 contacts the target at a suitabledistance upon exiting the end of the nozzle 153. For example, the firstprint material 122 may exit the end of the nozzle 153 and the terminaland 123 of the first print material 122 may contact the target 125. Inparticular instances, controlling the dispense gap 163 can includecontrolling the height of the end of the nozzle 153 above the target125, such that print material can contact the target upon exiting thenozzle 153 without forming a free droplet in the space between the endof the nozzle 153 and the target 125. It is been noted that for certaintypes of print material, including those suitable for forming the shapedabrasive particle, the deposition process should be conducted to avoidthe formation of free droplets, and during deposition a connection ismaintained between the target 125 and the end of the nozzle 153 by thefirst print material 122.

Furthermore, suitable formation of the body of the shaped abrasiveparticle can include controlling the dispense gap by varying theZ-directional distance between the end of the nozzle 153 and the target125 based upon at least one of the parameters of the group includingnozzle tip length 161, the nozzle width 162, the deposition pressure,the deposition rate, the deposition volume, the deposition position, thefilling pattern of the print material, the dynamic yield stress of theprint material, the static yield stress of the print material, the yieldstress ratio of the print material, the viscosity of the print material,and a combination thereof. According to one embodiment, the process offorming the body can include controlling the dispense gap 163 by varyingthe dispense gap based upon the deposition pressure. In other instances,the process s of forming the body can include controlling the dispensegap 163 by varying the dispense gap 163 based upon the depositionposition. In still other embodiments, the process of forming may includevarying the dispense gap 163 depending on the deposition position, andmore particularly, based on the resolution of the feature desired at theparticular deposition position. For example, if the material is to bedeposited at a position representing a corner or edge of the body of theshaped abrasive particle, the dispense gap 163 may be adjusted, and maybe different compared to a dispense gap 163 used to form a major surfaceor interior portion of the body of the shaped abrasive particle.Furthermore, the process of controlling the dispense gap 163 can includevarying the dispense gap 163 to control the volume of material depositedat a deposition position, which may be suitable for formation of certainfeatures of the body, including for example, a corner, an edge, a majorsurface, or interior portion of the body.

In accordance with an embodiment, the process of forming the body of theshaped abrasive particle using the additive manufacturing process caninclude controlling a filling pattern that defines the order of formingthe portions of the body. The filling pattern and particular processassociated with the filling pattern can be selected to form a suitableshaped abrasive particle and may facilitate improved performance of theshaped abrasive particle and fixed abrasives incorporating the shapedabrasive particle. As noted in the embodiments herein, the first portion141 may be formed into a two-dimensional or three-dimensional shapedepending upon the desired shape of the first portion 141 and the finalshape of the shaped abrasive particle. Any one of the portions of theshaped abrasive particle (e.g., the first portion 141) can be formed ina particular order defined by a filling pattern. The filling pattern candefine a deposition process including but not limited to an outside-infilling process, an inside-out filling process, a side-to-side fillingprocess, a bottom-up filling process, and a combination thereof.

For example, referring to FIG. 1C, a top-down view of a filling patternfor forming a portion of a shaped abrasive particle according to anembodiment is provided. As illustrated, the first portion 181 can be inthe form of a layer and may be formed by initiating deposition of theprint material at the position 182. The deposition assembly and theprocess of depositing the print material may traverse along the path 187in the direction 184 from the position 182 to the position 183, wherethe deposition process is stopped and the first portion 181 iscompleted. Such a filling pattern can be an outside-in filling process.The outside-in filling process can be characterized by a process thatinitially forms at least a portion of an outer periphery 185 of thefirst portion 181 and subsequently forms the interior portion 186.

In another embodiment, an inside-out filling process may be utilizedthat can include a process of depositing the print material to initiallyform an interior region of a portion and subsequently forming theperipheral regions of the portion. For example, referring again to FIG.1C, a filling pattern using an inside-out filling process can beundertaken in the opposite direction of the outside-in filling process.The inside-out filling process can initiate deposition at the position183 and traverse along the path 187 in the direction opposite thedirection 184 to the position 182 where the deposition process can bestopped and the first portion 181 is formed. In such an embodiment, theinterior portion 186 of the first portion 181 is formed first and theouter periphery 185 of the first portion 181 is formed subsequent to andaround the interior portion 186.

Referring to FIG. 1D, a side-to-side filling process is illustratedaccording to an embodiment. In a side-to-side filling process, thedeposition assembly can initiate deposition of the print material atposition 187, and move laterally back and forth depositing the printmaterial and stopping at position 188 to form a first portion.

FIG. 1D can also represent an embodiment of a bottom-up filling processin another embodiment. It will be appreciated that for a bottom-upfilling process, the print material can be deposited in a pattern thatis based upon formation of one or more overlying layers. For example, ina bottom-up filling process, the deposition assembly may initiatedeposition of the print material at position 187 and move back and forthbuilding the structure upon itself in a vertical direction and endingthe deposition process at position 188.

The process of forming the body can include controlling a fillingpattern such that a first portion of the body formed at a first time canbe formed using a first filling pattern, and a second portion of thebody formed a second time, which is distinct from the first time, can beformed using a second filling pattern that is distinct from the firstfilling pattern. For example, in one particular embodiment, the fillingpattern used to form the body can include forming a first portion by anoutside-in filling process and a second portion by an inside-out fillingprocess. More particularly, referring again to FIG. 1C, a first portion181 in the form of a first layer can be formed by an outside-in formingprocess and subsequently a second portion can be formed over the firstportion 181. The second portion can be in the form of a layer overlyingthe first portion 181, and the second portion can be formed by aninside-out filling process, wherein deposition can be initiated at aposition directly above position 183 and concluded at a positiondirectly above position 182.

According to a particular embodiment, the print material, which caninclude a mixture, can have a particular dynamic yield stress (σd) thatmay facilitate suitable formation of the body of the shaped abrasiveparticle. For example, the print material may have a dynamic yieldstress (σd) of at least about 100 Pa, at least about 120 Pa, at leastabout 140 Pa, at least about 160 Pa, at least about 180 Pa, at leastabout 200 Pa. Still, in another non-limiting embodiment, the printmaterial may have a dynamic yield stress (σd) of not greater than about1500 Pa, not greater than about 1300 Pa, not greater than about 1200 Pa,not greater than about 1100 Pa, not greater than about 1000 Pa. It willbe appreciated that the print material can have a dynamic yield stress(σd) within a range between any of the minimum maximum values above,including for example, at least about 100 Pa and not greater than about1500 Pa, at least about 160 Pa and not greater than about 1200 Pa, oreven at least about 200 Pa, and not greater than about 1200 Pa.

The process of forming the body can include controlling at least oneprocess parameter such as the dispense gap, the nozzle tip length, thenozzle width, the deposition pressure, the deposition rate, thedeposition volume, the deposition position, and the filling pattern ofthe print material based on the dynamic yield stress (σd) of the printmaterial. It will be appreciated that the process can includecontrolling a combination of the foregoing process parameters based onthe dynamic yield stress. Control of one or more process parametersbased on the dynamic yield stress may facilitate improved formation of ashaped abrasive particle.

In another embodiment, the print material, which may include a mixture,may have a particular static yield stress (σs) that may facilitatesuitable formation of the body of the shaped abrasive particle. Forexample, the may have a static yield stress (σs) of at least about 180Pa, such as at least about 200 Pa, at least about 250 Pa, at least about300 Pa, at least about 350 Pa, at least about 400 Pa, at least about 450Pa, at least about 500 Pa, at least about 550 Pa, at least about 600 Pa.In another non-limiting embodiment, the static yield stress (σs) can benot greater than about 20,000 Pa, such as not greater than about 18,000Pa, not greater than about 15,000 Pa, not greater than about 5000 Pa,not greater than about 1000 Pa. It will be appreciated that the printmaterial can have a static yield stress (σs) within a range between anyof the minimum and maximum values noted above, including for example, atleast about 180 Pa and not greater than about 20,000 Pa, at least about400 Pa and not greater than about 18,000 Pa, or even at least about 500Pa and not greater than about 5000 Pa.

The process of forming the body can include controlling at least oneprocess parameter such as the dispense gap, the nozzle tip length, thenozzle width, the deposition pressure, the deposition rate, thedeposition volume, the deposition position, and the filling pattern ofthe print material based on the static yield stress (σs) of the printmaterial. It will be appreciated that the process can includecontrolling a combination of the foregoing process parameters based onthe static yield stress. Control of one or more process parameters basedon the static yield stress may facilitate improved formation of a shapedabrasive particle.

In certain instances, the process of forming the body of the shapedabrasive particle can include forming a print material having aparticular relationship between the static yield stress (σs) and thedynamic yield stress (σd). In one embodiment, the print material may beformed such that the static yield stress is different than the dynamicyield stress. More particularly, the print material may be formed suchthat it is a shear-thinning print material configured to be suitablyextruded from the nozzle and yet have control dimensional stability toavoid significant movement (e.g., slumping) once deposited on thetarget.

In one embodiment, the print material, which may include a mixture, canhave a static yield stress that is greater than the dynamic yield stressthat may facilitate formation of the shaped abrasive particle. Moreparticularly, the print material may be formed such that it has aparticular yield stress ratio (σd/σs), such as not greater than about 1,not greater than about 0.99, not greater about 0.97, not greater thanabout 0.95, not greater than about 0.9, not greater than about 0.85, notgreater than about 0.8, not greater than about 0.75, not greater thanabout 0.7, not greater than about 0.65, not greater than about 0.6, notgreater than about 0.55, or even not greater than about 0.5. Still, inone non-limiting embodiment, the yield stress ratio (σd/σs) can be atleast about 0.01, such as at least about 0.05, at least about 0.08, atleast about 0.1, at least about 0.15, at least about 0.2, at least about0.25, at least about 0.3, at least about 0.35, at least about 0.4, oreven at least about 0.45, or even at least 0.5. It will be appreciatedthat the print material can have a yield stress ratio within a rangebetween any of the minimum and maximum values noted above, including forexample, a yield stress ratio of not greater than one and at least about0.01, such as not greater than about 0.97 and at least about 0.1, oreven not greater than about 0.8 and at least about 0.2.

The process of forming the body can include controlling at least oneprocess parameter such as the dispense gap, the nozzle tip length, thenozzle width, the deposition pressure, the deposition rate, thedeposition volume, the deposition position, and the filling pattern ofthe print material based on the yield stress ratio (σd/σs) of the printmaterial. It will be appreciated that the process can includecontrolling a combination of the foregoing process parameters based onthe yield stress ratio (σd/σs). Control of one or more processparameters based on the yield stress ratio (σd/σs) may facilitateimproved formation of a shaped abrasive particle.

In yet another embodiment, the print material may be formed to have aparticular viscosity to facilitate formation of the body of the shapedabrasive particle having the features of the embodiments herein. Forexample, the print material can have a viscosity of at least about 4×10³Pa s, such as at least about 5×10³ Pa s, at least about 6×10³ Pa s, atleast about 7×10³ Pa s, at least about 7.5×10³ Pa s. In anothernon-limiting embodiment, the print material can have a viscosity of notgreater than about 20×10³ Pa s, such as not greater than about 18×10³ Pas, not greater than about 15×10³ Pa s, or even not greater than about12×10³ Pa s. Still, it will be appreciated that the print material canhave a viscosity within a range including any of the minimum and maximumvalues noted above, including but not limited to, at least about 4×10³Pa s and not greater than about 20×10³ Pa s, such as at least about5×10³ Pa s and not greater than about 18×10³ Pa s, at least about 6×10³Pa s and not greater than about 15×10³ Pa s. For those print materialsthat are shear-thinning or otherwise non-Newtonian materials, the aboveviscosity values may be an apparent viscosity. The viscosity can bemeasured by incrementally decreasing a shear rate from 100 s⁻¹ to 2 s⁻¹without pre-shearing the print material using a parallel platerheometer.

The process of forming the body can include controlling at least oneprocess parameter such as the dispense gap, the nozzle tip length, thenozzle width, the deposition pressure, the deposition rate, thedeposition volume, the deposition position, and the filling pattern ofthe print material based on the viscosity of the print material. It willbe appreciated that the process can include controlling a combination ofthe foregoing process parameters based on the viscosity. Control of oneor more process parameters based on the viscosity may facilitateimproved formation of a shaped abrasive particle.

It will be appreciated that any of the forming processes herein can becombined with other processes, including conventional processes ofprinting, spraying, deposition, casting, molding, and the like. Incertain instances, the additive manufacturing process may be used toform a preform of the body of the shaped abrasive particle. The preformcan be a skeleton of the body, such as an outer portion or an innerportion that is first created, and processed further through one or moreother processes to create the shaped abrasive particle. For example, inat least one embodiment, an additive manufacturing process may be usedto form an exterior portion of the body, such as the peripheral walls ofthe body. After forming the exterior portion, a subsequent operation maybe utilized to form an interior portion of the body, including forexample, a separate forming process (e.g., a filling process) using thesame material or a different material used in the additive manufacturingprocess used to form the exterior portion. One suitable forming processto form the interior portion can include a spraying process or printingprocess. The two step process of forming the different portions of thebody may facilitate efficient processing over a process relying only onan additive manufacturing process to form the entire body of the shapedabrasive particle. It will be appreciated that the above example isnon-limiting and other two-step processes including the additivemanufacturing process may be used. It is envisioned that one may form aninterior portion of the body using the additive manufacturing processand forming an exterior portion of the body using a different processthan the additive manufacturing process.

The shaped abrasive particle formed by an additive manufacturing processas defined herein can include a variety of other suitable dimensions andfeatures. In an embodiment, the body of the shaped abrasive particleincludes a first major surface, a second major surface, and at least oneside surface extending between the first major surface and the secondmajor surface.

The bodies of the shaped abrasive particles can have a percent flashingthat may facilitate improved performance. Notably, the flashing definesan area of the body as viewed along one side, wherein the flashingextends from a side surface of the body 301 within the boxes 302 and303, as illustrated in FIG. 3. The flashing can represent taperedregions proximate to the upper surface 303 and bottom surface 304 of thebody 301. The flashing can be measured as the percentage of area of thebody 301 along the side surface contained within a box extending betweenan innermost point of the side surface (e.g., 321) and an outermostpoint (e.g., 322) on the side surface of the body 301. In one particularinstance, the body 301 can have a particular content of flashing, whichcan be the percentage of area of the body 301 contained within the boxes302 and 303 compared to the total area of the body 301 contained withinboxes 302, 303, and 304. The flashing can represent tapered regionsproximate to first and second major surfaces of the body. The flashingcan be measured as the percentage of area of the body along the sidesurface contained within a box extending between an innermost point ofthe side surface and an outermost point on the side surface of the body.

In one particular instance, the body can have a particular content offlashing, which can be the percentage of area of the body within thetapered regions compared to the total area of the body. According to oneembodiment, the percent flashing (f) of the body can be at least about1%. In another embodiment, the percent flashing can be greater, such asat least about 2%, at least about 3%, at least about 5%, at least about8%, at least about 10%, at least about 12%, such as at least about 15%,at least about 18%, or even at least about 20%. Still, in a non-limitingembodiment, the percent flashing of the body 301 can be controlled andmay be not greater than about 45%, such as not greater than about 40%,not greater than about 35%, not greater than about 30%, not greater thanabout 25%, not greater than about 20%, not greater than about 18%, notgreater than about 15%, not greater than about 12%, not greater thanabout 10%, not greater than about 8%, not greater than about 6%, or evennot greater than about 4%. In a particular embodiment, the body can beessentially free of flashing. It will be appreciated that the percentflashing of the body can be within a range between any of the aboveminimum and maximum percentages. Moreover, it will be appreciated thatthe above flashing percentages can be representative of an averageflashing percentage or a median flashing percentage for a batch ofshaped abrasive particles.

The shaped abrasive particles of the embodiments herein can be formedsuch that the body includes a crystalline material, and moreparticularly, a polycrystalline material. Notably, the polycrystallinematerial can include grains. In one embodiment, the body can beessentially free of an organic material including, for example, abinder. More particularly, the body can consist essentially of apolycrystalline material.

In one aspect, the body of the shaped abrasive particle can be anagglomerate including a plurality of particles, grit, and/or grainsbonded to each other to form the body. Suitable grains can includenitrides, oxides, carbides, borides, oxynitrides, oxyborides, diamond,and a combination thereof. In particular instances, the grains caninclude an oxide compound or complex, such as aluminum oxide, zirconiumoxide, titanium oxide, yttrium oxide, chromium oxide, strontium oxide,silicon oxide, and a combination thereof. In one particular instance,the ceramic article is formed such that the grains forming the bodyinclude alumina, and more particularly, may consist essentially ofalumina. In another instance, the body of the ceramic article canconsist essentially of alumina. Moreover, in particular instances, thebody of the shaped abrasive particle can be formed from a seeded solgel.

In an embodiment, the body can include a polycrystalline material. Thegrains (e.g., crystallites) contained within the body may have anaverage grain size that is generally not greater than about 100 microns.In other embodiments, the average grain size can be less, such as notgreater than about 80 microns, not greater than about 50 microns, notgreater than about 30 microns, not greater than about 20 microns, notgreater than about 10 microns, or even not greater than about 1 micron.Still, the average grain size of the grains contained within the bodycan be at least about 0.01 microns, such as at least about 0.05 microns,such as at least about 0.08 microns, at least about 0.1 microns, or evenat least about 0.5 microns. It will be appreciated that the grains canhave an average grain size within a range between any of the minimum andmaximum values noted above.

In accordance with certain embodiments, the shaped abrasive particle canbe a composite article including at least two different types of grainswithin the body. It will be appreciated that different types of grainsare grains having different compositions with regard to each other. Forexample, the body can be formed such that it includes at least twodifferent types of grains, wherein the two different types of grains canbe nitrides, oxides, carbides, borides, oxynitrides, oxyborides,diamond, and a combination thereof.

In some embodiments, the body of the ceramic article can include avariety of suitable additives. For example, the additive can include anoxide. In a particular embodiment, the additive can include a metalelement, such as a rare-earth element. In another particular embodiment,the additive can include a dopant material. For example, the dopantmaterial can include an element or compound selected from the groupconsisting of an alkali element, an alkaline earth element, a rare-earthelement, a transition metal element, and a combination thereof. In yetanother embodiment, the dopant material can include an element selectedfrom the group consisting of hafnium, zirconium, niobium, tantalum,molybdenum, vanadium, lithium, sodium, potassium, magnesium, calcium,strontium, barium, scandium, yttrium, lanthanum, cesium, praseodymium,chromium, cobalt, iron, germanium, manganese, nickel, titanium, zinc,and a combination thereof.

According to a particular embodiment, the forming process can formprecursor shaped abrasive particles. The precursor shaped abrasiveparticles may undergo further processing to form shaped abrasiveparticles. Such further processing can include, but need not be limitedto, drying, heating, evolving, volatilizing, sintering, doping, drying,curing, reacting, radiating, mixing, stirring, agitating, calcining,comminuting, sieving, sorting, shaping, and a combination thereof.

Drying may include removal of a particular content of material,including volatiles, such as water. In accordance with an embodiment,the drying process can be conducted at a drying temperature of notgreater than about 300° C., such as not greater than about 280° C., oreven not greater than about 250° C. Still, in one non-limitingembodiment, the drying process may be conducted at a drying temperatureof at least about 50° C. It will be appreciated that the dryingtemperature may be within a range between any of the minimum and maximumtemperatures noted above. Furthermore, the drying process may beconducted for a particular duration. For example, the drying process maybe not greater than about six hours.

The process of forming the precursor shaped abrasive particle to afinally-formed shaped abrasive particle may further comprise a sinteringprocess. Sintering of the precursor shaped abrasive particle may beutilized to densify the article, which is generally in a green state asthe precursor shaped abrasive particle. In a particular instance, thesintering process can facilitate the formation of a high-temperaturephase of the ceramic material. For example, in one embodiment, theprecursor shaped abrasive particle may be sintered such that ahigh-temperature phase of the material is formed, including for example,alpha alumina. According to one particular embodiment, the shapedabrasive particle can be a shaped abrasive particle having at leastabout 90 wt % alpha alumina for the total weight of the particle. In amore particular instance, the content of alpha alumina may be greatersuch that the shaped abrasive particle may consist essentially of alphaalumina.

In accordance with another aspect, a method of forming a fixed abrasivearticle including shaped abrasive particles formed through the additivemanufacturing process can also be accomplished. For example, the processof forming a fixed abrasive article can include forming a plurality ofshaped abrasive particles on a substrate, where each of the shapedabrasive particles of the plurality of shaped abrasive particles have abody formed by an additive manufacturing process. It will be appreciatedthat the fixed abrasive article may include a bonded abrasive article, acoated abrasive article, and the like. It will further be appreciatedthat the substrate can include, for example, a backing.

In at least one embodiment, the forming process can be conducted suchthat the shaped abrasive particles are formed directly overlying thesubstrate. For example, in accordance with an embodiment, a perspectiveview illustration of a fixed abrasive article including shaped abrasiveparticles overlying the substrate is provided in FIG. 2. As illustrated,the fixed abrasive article 200 can include a first shaped abrasiveparticle 201 overlying a substrate 204 and a second shaped abrasiveparticle 211 overlying the substrate 204.

It will be appreciated that the process of forming a shaped abrasiveparticle as part of a fixed abrasive article can include any of theprocesses described herein in other embodiments. For example, asindicated herein, the body of each of the shaped abrasive particles 201and 211 of the plurality of shaped abrasive particles can be formedaccording to a digital model. As further illustrated, and describedherein, each of the shaped abrasive particles 201 and 211 can havebodies formed from a plurality of portions 203, which may be discretefrom each other, or may have undergone further processing (e.g.,modifying) to join the portions together to form each of the bodies ofthe shaped abrasive particles 201 and 211.

As described in the embodiments herein, the additive manufacturingprocess of forming the body according to a digital model can includedepositing a first print material as a first portion of the body of eachof the shaped abrasive particles of the plurality of shaped abrasiveparticles at a first time. Furthermore, the process can includedepositing a second print material as a second portion of the body ofeach of the shaped abrasive particles of the plurality of shapedabrasive particles at a second time that is different than the firsttime. In a particular embodiment, the additive manufacturing processalso can include preferentially modifying one of the first portion andthe second portion to join the first portion and the second portion andform a subsection of the body of the shaped abrasive particle.

In accordance with a particular embodiment, the forming process can beconducted directly on at least a portion of a bonding layer 231, whichmay be overlying the substrate. The bonding layer 231 can include amaterial such as an inorganic material, a vitreous material, acrystalline material, an organic material, a resin material, a metalmaterial, a metal alloy, and a combination thereof. The bonding layermay be a continuous layer or material or may be a discontinuous layer ofmaterial having discrete bonding regions separated by gaps, whereinessentially no bonding material is present. The process of forming caninclude selectively forming shaped abrasive particles in regionscorresponding to the discrete bonding regions, such that each discretebonding region has one or more shaped abrasive particles containedtherein.

In some embodiments of the forming process, the substrate 204 may betranslated through a forming zone. In the forming zone, at least oneshaped abrasive particle of the plurality of shaped abrasive particlescan be formed overlying the substrate. In particular instances, thetranslation of the substrate 204 can include a stepped translationprocess, wherein the substrate 204 may be translated a certain distanceand stopped to allow the formation of the shaped abrasive particle tooccur. After a shaped abrasive particle is suitably formed overlying thesubstrate 204, the stepped translation process can continue bytranslating the substrate 204 in a desirable direction by a knowndistance again and stopping again to facilitate the formation of anothershaped abrasive particle at a particular location on substrate 204. Inone embodiment, as shown in FIG. 2, the substrate 204 may be translatedto a first position defined by the position of the shaped abrasiveparticle 211, wherein at a first time the shaped abrasive particle 211can be formed by an additive manufacturing process. After suitableformation of the shaped abrasive particle 211, the substrate 204 may betranslated in a direction to a position identified by the position ofthe shaped abrasive particle 201 overlying the substrate 204. At thatpoint, the substrate 204 may be stopped to allow the formation of theshaped abrasive particle 201 at the location provided in FIG. 2.

As such, a plurality of shaped abrasive particles can be formed atpredetermined locations on the substrate 204. Notably, in certaininstances, the formation of the fixed abrasive article 200 can beconducted such that each of the shaped abrasive particles can be placedon the backing, and such placement can be conducted simultaneously withthe formation of the body of each of the shaped abrasive particles.

Furthermore, it will be appreciated that such a process of forming afixed abrasive article also can include orienting each of the shapedabrasive particles of the plurality of the shaped abrasive particlesrelative to the substrate. Such orienting can facilitate the controlledorientation of each of the shaped abrasive particles relative to eachother as well as relative to the substrate 204. For example, the processof forming the body of a shaped abrasive particle can be conductedsimultaneously with the process of orienting the shaped abrasiveparticle relative to the substrate 204.

In more particular instances, each shaped abrasive particle may beformed in a manner such that it has a controlled orientation withrespect to a vertical orientation, a rotational orientation, a flatorientation, or a side orientation. In the flat orientation, a bottomsurface of a shaped abrasive particle can be closest to a surface of thesubstrate 204 (e.g., a backing) and an upper surface of the shapedabrasive particle can be directed away from the substrate 204 andconfigured to conduct initial engagement with a workpiece. Note hereinthat vertical orientation can refers to the orientation of the particlesas viewed in a plane perpendicular to the belt, whereas rotationalorientation refer to the orientation of a shaped abrasive particle asviewed in a plane parallel to the belt.

Turning briefly to FIG. 4, a coated abrasive article is illustratedincluding shaped abrasive particles in a particular orientation relativeto the substrate. For example, the coated abrasive article 400 caninclude a substrate 401 (i.e., a backing) and at least one adhesivelayer overlying a surface of the substrate 401. The adhesive layer caninclude a make coat 403 and/or a size coat 404. The coated abrasive 400can include abrasive particulate material 410, which can include shapedabrasive particles 405 of the embodiments herein and a second type ofabrasive particulate material 407 in the form of diluent abrasiveparticles having a random shape, which may not necessarily be shapedabrasive particles. The make coat 403 can be overlying the surface ofthe substrate 401 and surrounding at least a portion of the shapedabrasive particles 405 and second type of abrasive particulate material407. The size coat 404 can be overlying and bonded to the shapedabrasive particles 405 and second type of abrasive particulate material407 and the make coat 403.

According to one embodiment, the shaped abrasive particles 405 hereincan be oriented in a predetermined orientation relative to each otherand the substrate 401. As illustrated in FIG. 4, the shaped abrasiveparticles 405 can be oriented in a flat orientation relative to thesubstrate 401. In the flat orientation, the bottom surface 414 of theshaped abrasive particles can be closest to a surface of the substrate401 (i.e., the backing) and the upper surface 413 of the shaped abrasiveparticles 405 can be directed away from the substrate 401 and configuredto conduct initial engagement with a workpiece.

According to another embodiment, the shaped abrasive particles 505 canbe placed on a substrate 501 in a predetermined side orientation, suchas that shown in FIG. 5. In particular instances, a majority of theshaped abrasive particles 505 of the total content of shaped abrasiveparticles 505 on the abrasive article 500 can have a predetermined sideorientation. In the side orientation, the bottom surface 414 of theshaped abrasive particles 505 can be spaced away and angled relative tothe surface of the substrate 501. In particular instances, the bottomsurface 414 can form an obtuse angle (A) relative to the surface of thesubstrate 501. Moreover, the upper surface 513 can be spaced away andangled relative to the surface of the substrate 501, which in particularinstances, may define a generally acute angle (B). In a sideorientation, a side surface 416 of the shaped abrasive particle can beclosest to the surface of the substrate 501, and more particularly, maybe in direct contact with a surface of the substrate 501.

According to another embodiment, one or more shaped abrasive particlescan be placed on a substrate in a predetermined side orientation. Inparticular instances, a majority of the shaped abrasive particles of theplurality of shaped abrasive particles on the abrasive article can havea predetermined side orientation. In the side orientation, a bottomsurface of the shaped abrasive particle can be spaced away and angledrelative to the surface of the substrate 204. In particular instances,the bottom surface can form an obtuse angle relative to the surface ofthe substrate 204. Moreover, the upper surface of the shaped abrasiveparticle is spaced away and angled relative to the surface of thesubstrate 204, which in particular instances, may define a generallyacute angle. In a side orientation, one or more side surfaces of theshaped abrasive particle can be closest to the surface of the substrate204, and more particularly, may be in direct contact with a surface ofthe substrate 204.

For certain fixed abrasive articles herein, at least about 55% of theplurality of shaped abrasive particles on the fixed abrasive article 200can be oriented in a side orientation. Still, the percentage may begreater, such as at least about 60%, at least about 65%, at least about70%, at least about 75%, at least about 77%, at least about 80%, atleast about 81%, or even at least about 82%. And for one non-limitingembodiment, a fixed abrasive article 200 may be formed using the shapedabrasive particles herein, wherein not greater than about 99% of theplurality of shaped abrasive particles are oriented in a sideorientation.

Furthermore, the abrasive articles made with the shaped abrasiveparticles formed by the additive manufacturing processes describedherein can utilize various contents of the shaped abrasive particles.For example, the fixed abrasive articles can be coated abrasive articlesincluding a single layer of the shaped abrasive particles in an opencoat configuration or a closed coat configuration. For example, theplurality of shaped abrasive particles can define an open coat abrasiveproduct having a coating density of shaped abrasive particles of notgreater than about 70 particles/cm². In other instances, the density ofshaped abrasive particles per square centimeter of the open coatabrasive article may be not greater than about 65 particles/cm², such asnot greater than about 60 particles/cm², not greater than about 55particles/cm², or even not greater than about 50 particles/cm². Still,in one non-limiting embodiment, the density of the open coat coatedabrasive using the shaped abrasive particles herein can be at leastabout 5 particles/cm², or even at least about 10 particles/cm². It willbe appreciated that the density of shaped abrasive particles per squarecentimeter of an open coat coated abrasive article can be within a rangebetween any of the above minimum and maximum values.

In an alternative embodiment, the plurality of shaped abrasive particlescan define a closed coat abrasive product having a coating density ofshaped abrasive particles of at least about 75 particles/cm², such as atleast about 80 particles/cm², at least about 85 particles/cm², at leastabout 90 particles/cm², at least about 100 particles/cm². Still, in onenon-limiting embodiment, the density of the closed coat coated abrasiveusing the shaped abrasive particle herein can be not greater than about500 particles/cm². It will be appreciated that the density of shapedabrasive particles per square centimeter of the closed coat abrasivearticle can be within a range between any of the above minimum andmaximum values.

The substrate of the fixed abrasive articles described herein caninclude a variety of suitable materials, including an organic materialsuch as polymers, an inorganic material, such as metal, glass, ceramic,and a combination thereof. In certain instances, the substrate caninclude a woven material. However, the substrate may be made of anon-woven material. In another embodiment, the substrate can include amaterial selected from the group consisting of cloth, paper, film,fabric, fleeced fabric, vulcanized fiber, woven material, non-wovenmaterial, webbing, polymer, resin, phenolic resin, phenolic-latex resin,epoxy resin, polyester resin, urea formaldehyde resin, polyester,polyurethane, polypropylene, polyimides, and a combination thereof.

In certain situations, the shaped abrasive particles may be placed on afirst substrate, which facilitates further processing of the shapedabrasive particles, such as drying, heating, and sintering. Thesubstrate may be a permanent article. However, in other instances, thesubstrate may be a sacrificial article, that can be partially orcompletely destroyed during further processing of the shaped abrasiveparticles. The first substrate may be combined with a second substrateafter processing of the shaped abrasive particles, for later forming theabrasive article. For example, in instances using a permanent firstsubstrate, the first substrate may be combined with the second substrateto form a composite substrate that is used in the finally-formed fixedabrasive article. In still other instances where a sacrificial substrateis used, the placement and orientation of the shaped abrasive particleson the first substrate may be substantially maintained through theforming process, even though the first substrate is partially orcompletely removed. The finally-formed shaped abrasive particles may becombined with a second substrate while maintaining their placement andorientation to facilitate formation of the finally-formed abrasivearticle.

In some embodiments, the substrate of the fixed abrasive articles alsocan include a suitable additive or additives. For example, the substratecan include an additive chosen from the group consisting of catalysts,coupling agents, curants, anti-static agents, suspending agents,anti-loading agents, lubricants, wetting agents, dyes, fillers,viscosity modifiers, dispersants, defoamers, and grinding agents.

The fixed abrasive articles described herein, in addition to including asubstrate (e.g., a backing), can include at least one adhesive layer,such as a bonding layer, overlying a surface of the substrate. Theadhesive layer can include a make coat. A polymer formulation may beused to form any of a variety of layers of the abrasive article such as,for example, a frontfill, a pre-size, the make coat, the size coat,and/or a supersize coat. When used to form the frontfill, the polymerformulation generally includes a polymer resin, fibrillated fibers(preferably in the form of pulp), filler material, and other optionaladditives. Suitable formulations for some frontfill embodiments caninclude material such as a phenolic resin, wollastonite filler,defoamer, surfactant, a fibrillated fiber, and a balance of water.Suitable polymeric resin materials include curable resins selected fromthermally curable resins including phenolic resins, urea/formaldehyderesins, phenolic/latex resins, as well as combinations of such resins.Other suitable polymeric resin materials may also include radiationcurable resins, such as those resins curable using electron beam, UVradiation, or visible light, such as epoxy resins, acrylated oligomersof acrylated epoxy resins, polyester resins, acrylated urethanes andpolyester acrylates and acrylated monomers including monoacrylated,multiacrylated monomers. The formulation can also comprise a nonreactivethermoplastic resin binder which can enhance the self-sharpeningcharacteristics of the deposited abrasive composites by enhancing theerodibility. Examples of such thermoplastic resin include polypropyleneglycol, polyethylene glycol, and polyoxypropylene-polyoxyethene blockcopolymer, etc. Use of a frontfill on the substrate can improve theuniformity of the surface, for suitable application of the make coat andimproved application and orientation of shaped abrasive particles in apredetermined orientation.

The abrasive article also can include abrasive particulate material,which can include shaped abrasive particles of the embodiments hereinand a second type of abrasive particulate material in the form ofdiluent abrasive particles having a random shape, which may notnecessarily be shaped abrasive particles. In an embodiment, the makecoat can be overlying the surface of the substrate and surrounding atleast a portion of the shaped abrasive particles and second type ofabrasive particulate material. In another embodiment, the make coat canbe bonded directly to at least a portion of the substrate. The make coatcan include a variety of suitable materials including, for example, anorganic material, a polymeric material, or a material selected from thegroup consisting of polyesters, epoxy resins, polyurethanes, polyamides,polyacrylates, polymethacrylates, poly vinyl chlorides, polyethylene,polysiloxane, silicones, cellulose acetates, nitrocellulose, naturalrubber, starch, shellac, and a combination thereof.

The adhesive layer also can include a size coat. The size coat can beoverlying at least a portion of the plurality of shaped abrasiveparticles described herein, as well as any second type of abrasiveparticulate material and the make coat. The size coat also can be bondeddirectly to at least a portion of the plurality of shaped abrasiveparticles. Like the make coat, the size coat can include a variety ofsuitable materials including, for example, an organic material, apolymeric material, or a material selected from the group consisting ofpolyesters, epoxy resins, polyurethanes, polyamides, polyacrylates,polymethacrylates, poly vinyl chlorides, polyethylene, polysiloxane,silicones, cellulose acetates, nitrocellulose, natural rubber, starch,shellac, and a combination thereof.

The fixed abrasive articles, including the shaped abrasive particles andthe additive manufacturing processes used to form the shaped abrasiveparticles as described herein represent a departure from and improvementover conventional fixed abrasive articles. While many processes offorming shaped abrasive particles, including shaped abrasive particles,rely primarily on templating and/or substractive processes (e.g.,molding, screen printing, etc.), the processes disclosed in theembodiments herein include a forming process for forming shaped abrasiveparticles using an additive manufacturing process. Moreover, theprocesses may further utility a digital model, which can be used toanalyze, compare, and adapt the forming process, which may facilitateimproved dimensional uniformity, shape, placement, and ultimatelyperformance of the article utilizing the shaped abrasive particles.

While it will be appreciated that the shaped abrasive particles of theembodiments can have any suitable shape, FIGS. 6 through 19 provideillustrations of some exemplary, non-limiting shaped abrasive particlesthat may be made according to the embodiments herein.

In particular, in one embodiment provided in FIG. 18, the shapedabrasive particle 1800 can include a body 1801 including a first layer1802 and a second layer 1803 overlying the first layer 1802. Accordingto an embodiment, the body 1801 can have layers 1802 and 1803 that arearranged in a stepped configuration relative to each other. A steppedconfiguration can be characterized by at least one plateau region 1820on a surface 1810 of the first layer 1802 between a side surface 1804 ofthe first layer 1802 and a side surface 61805 of the second layer 1803.The size and shape of the plateau region 1820 may be controlled orpredetermined by one or more processing parameters and may facilitate animproved deployment of the abrasive particles into an abrasive articleand performance of the abrasive article.

In one embodiment, the plateau region 1802 can have a lateral distance1821, which can be defined as the greatest distance between an edge 1807between the upper surface 1810 of the first layer 1802 and a sidesurface 1804 of the first layer to the side surface 1805 of the secondlayer. Analysis of the lateral distance 1821 may be facilitated by atop-view image of the body 1801, such as shown in FIG. 19. Asillustrated, the lateral distance 1821 can be the greatest distance ofthe plateau region 1802. In one embodiment, the lateral distance 1821may have a length that is less than the length 1810 of the first layer1802 (i.e., larger layer). In particular, the lateral distance 1821 canbe not greater than about 90%, such as not greater than about 80%, notgreater than about 70%, not greater than about 60%, not greater thanabout 50%, not greater than about 40%, not greater than about 30%, oreven not greater than about 20% of the length 1810 of the first layer1802 of the body 1801. Still, in one non-limiting embodiment, thelateral distance 1821 can have a length that is at least about 2%, atleast about 5%, at least about 8%, at least about 10%, at least about20%, at least about 25%, at least about 30%, or even at least about 50%of the length of the first layer 1802 of the body 1801. It will beappreciated that the lateral distance 1821 can have a length within arange between any of the minimum and maximum percentages noted above.

The second layer 1803 can have a particular length 1809, which is thelongest dimension of a side, such as shown in FIG. 19, relative to alength 1810 of the first layer 1802 that may facilitate improveddeployment of the abrasive particles into an abrasive article and/orperformance of the abrasive article. For example, the length 1809 of thesecond layer 1803 can be not greater than about 90%, such as not greaterthan about 80%, not greater than about 70%, not greater than about 60%,not greater than about 50%, not greater than about 40%, not greater thanabout 30%, or even not greater than about 20% of the length 1810 of thefirst layer 1802 of the body 1801. Still, in one non-limitingembodiment, the second layer 1803 can have a length 1809 that can be atleast about 2%, at least about 10%, at least about 20%, at least about30%, at least about 40%, at least about 50%, at least about 60%, or evenat least about 70% of the length 1810 of the first layer 1802 of thebody 1801. It will be appreciated that the length 1809 of the secondlayer 1803 relative to the length 1810 of the first layer 1802 can bewithin a range between any of the minimum and maximum percentages notedabove.

The foregoing shaped abrasive particle of FIGS. 18 and 19 can be formedusing the additive manufacturing process according to the embodimentsherein. Moreover, it is contemplated that the organization of the layerscan be different than as illustrated. The body may include anycombination of layers of different dimensions and/or shapes in anyorganization relative to each other.

Moreover, coated abrasive articles have been described in detail herein,but it will be appreciated that the shaped abrasive particles of theembodiments may be employed in bonded abrasive articles. Bonded abrasivearticles can take various shapes including wheels, discs, cups,segments, and the like generally consisting of composites havingabrasive grains contained within a three-dimensional bond matrix.Additionally, the bonded abrasive tools can include some volumepercentage of porosity.

Some suitable materials for use as the bond material can include metalmaterials, polymer materials (e.g., resin), vitreous or amorphous phasematerials, crystalline phase materials, and a combination thereof.

Bonded abrasive articles are typically formed from an initial mixtureincluding the bond material or a precursor of the bond material, theabrasive particles (e.g., shaped abrasive particles, diluent particles,combination of different types of abrasive particles, etc.), and fillers(e.g., active fillers, grinding aids, pore formers, mixing aids,reinforcing agents, etc.). The mixture can be formed into a green body(i.e., unfinished body) using various techniques, including but notlimited to, molding, pressing, extruding, depositing, casting,infiltrating, and a combination thereof. The green body may undergofurther processing to aid formation of the final-formed bonded abrasivebody. The processing may depend on the composition of the mixture, butcan include processes such as drying, curing, radiating, heating,crystallizing, re-crystallizing, sintering, pressing, decomposition,dissolution, and a combination thereof.

The final-formed bonded abrasive article may have various contents ofthe components (i.e., abrasive particles, bond material, filler, andporosity) depending on the intended end use. For example, in certaininstances, the final-formed bonded abrasive article can have a porosityof at least about 5 vol % of the total volume of the bonded abrasivearticle. In other embodiments, the porosity can be greater, such as onthe order of at least about 15 vol %, at least 25 vol %, at least about25 vol %, at least about 50 vol %, or even at least about 60 vol %.Particular embodiments may utilize a range of porosity between about 5vol % and about 75 vol % of the total volume of the bonded abrasivearticle.

Moreover, the final-formed bonded abrasive may have a content of bondmaterial of at least about 10 vol % for the total volume of the bondedabrasive body. In other instances, the body can include at least about30 vol %, such as at least about 40 vol %, at least about 50 vol % oreven at least about 60 vol % bond material for the total volume of thebody of the bonded abrasive article. Certain embodiments may utilize arange of bond material between about 10 vol % and about 90 vol %, suchas between about 10 vol % and about 80 vol %, or even between about 20vol % and about 70 vol % of the total volume of the bonded abrasivearticle.

The final-formed bonded abrasive may have a content of abrasiveparticles of at least about 10 vol % for the total volume of the bondedabrasive body. In other instances, the body can include at least about30 vol %, such as at least about 40 vol %, at least about 50 vol % oreven at least about 60 vol % abrasive particles for the total volume ofthe body of the bonded abrasive article. In other examples, the abrasivearticle may utilize a range of abrasive particles between about 10 vol %and about 90 vol %, such as between about 10 vol % and about 80 vol %,or even between about 20 vol % and about 70 vol % of the total volume ofthe bonded abrasive article.

Certain features, for clarity, described herein in the context ofseparate embodiments, may also be provided in combination in a singleembodiment. Conversely, various features that are, for brevity,described in the context of a single embodiment, may also be providedseparately or in any subcombination. Further, reference to values statedin ranges includes each and every value within that range.

In accordance with one aspect, the shaped abrasive particles of theembodiments herein can have bodies including various featuresfacilitated by the additive manufacturing process. For example, in oneembodiment the shaped abrasive particle may have a body having at leastone major surface having a self-similar feature. FIG. 20 includes aperspective view illustration of a shaped abrasive particle according toan embodiment. As illustrated, the shaped abrasive particle 2000 caninclude a body 2001 having an upper major surface 2002, a lower majorsurface 2004, and side surfaces 2005, 2006, and 2007 extending betweenthe major surfaces 2002 and 2004. FIG. 21 includes a top view of a majorsurface of the shaped abrasive particle 2000 of FIG. 20.

As illustrated, and in accordance with an embodiment, the major surface2002 of the shaped abrasive particle 2000 can have a self-similarfeature 2003. A self-similar feature 2003 can be an arrangement offeatures on a surface of the body of the shaped abrasive particle, suchas a major surface of the body. The self-similar feature can include oneor more features that can be arranged relative to each other, such as ina particular distribution, such as features arranged in a patternrelative to each other. The self-similar feature 2003 can include aplurality of shapes disposed on the major surface 2002 of the body 2001.In more particular instances, the self-similar feature 2003 can includea plurality of two-dimensional shapes nested within each other on themajor surface 2002. For example, in the embodiment illustrated in FIGS.20 and 21, the self-similar feature 2003 can include a plurality oftwo-dimensional triangular shapes patterned on the surface, anddistributed relative to each other in a nested arrangement, includingthe plurality of triangles 2009 and 2010.

In another embodiment, the self-similar feature can include arrangementof two-dimensional shapes at the major surface of the body of the shapedabrasive particle wherein the arrangement of the two-dimensional shapesare substantially the same two-dimensional shape as the two-dimensionalshape defined by a periphery of the major surface. For example,referring to the embodiments of FIGS. 20 and 21, the triangles 2009 and2010 can have substantially the same two-dimensional shape as thetwo-dimensional shape of the periphery 2012 of the upper major surface2002 of the shaped abrasive particle 2000. It will be appreciated thatwhile the embodiments of FIGS. 20 and 21 illustrate a shaped abrasiveparticle having a generally triangular two-dimensional shape, othertwo-dimensional shapes may be formed using the additive manufacturingprocess. For example, the body of the shaped abrasive particle caninclude a two-dimensional shape from the group including a regularpolygons, irregular regular polygons, irregular shapes, triangles,quadrilaterals, rectangles, trapezoid, pentagons, hexagons, heptagons,octagons, ellipses, Greek alphabet letters, Latin enough alphabetcharacters, Russian alphabet characters, Kanji characters, and acombination thereof.

Referring to FIG. 22, a top view image of a portion of the shapedabrasive particle of FIG. 20 is provided. The shaped abrasive particle2000 can include a corner 2201 which when viewed top-down can define aparticular radius of curvature. Notably, the corner 2201 can have anarcuate contour 2202 to which a best-fit circle 2203 may be fit. Thebest-fit circle 2203 may have a radius 2204 that can define the cornerroundness of the corner 2201. The best fit circle may be fit and theradius evaluated using a suitable form of imaging and magnification,such as provided in FIG. 22. Suitable software, such as ImageJ may beused.

In one embodiment, the body of a shaped abrasive particle can have aparticular corner roundness that may facilitate use in abrasiveoperations. For example, the shaped abrasive particle can have a bodyhaving a corner roundness of not greater than about 250 microns, such asnot greater than about 220 microns, not greater than about 200 microns,not greater than about 180 microns, not greater than about 160 microns,not greater than about 140 microns, not greater than about 120 microns,not greater than about 100 microns, not greater than about 90 microns,not greater than about 80 microns, not greater than about 70 microns,not greater than about 60 microns, not greater than about 50 microns,not greater than about 40 microns, not greater than about 30 microns, oreven not greater than about 20 microns. In one non-limiting embodiment,the body of the shaped abrasive particle can have a corner roundness ofat least about 0.1 microns, such as at least about 0.5 microns. It willbe appreciated that the body can have a corner roundness within a rangeincluding any of the minimum and maximum values noted above, includingfor example at least about 0.1 microns and not greater than about 250microns, such as at least about 0.1 microns and not greater than about100 microns, or even at least about 0.5 μm and not greater than about 80microns.

In accordance with another embodiment, the shaped abrasive particle canhave at least one major surface defining a concave, stepped surface. Forexample, referring to FIG. 23 a portion of a major surface of the shapedabrasive particle of FIG. 20 is provided. As provided, the major surface2002 can have a concave, stepped surface, which may be defined by aplurality of step features 2301 extending along at least a portion ofthe length of the body 2001. In a particular embodiment, the concave,stepped surface can define a thickness at a midpoint 2302 that is lessthan a thickness (t) of the body at an edge. It will be appreciated thatthe thickness (t) can extend in a direction perpendicular to the majorsurface 2002 of the body 2001 along the side surface 2005. In accordancewith a particular embodiment, the concave, stepped surface can includestep features 2301 including a plurality of flats 2304 and risers 2305,were in the flats extend substantially parallel to the plane of themajor surface 2002 and the risers 2305 extend substantiallyperpendicular to the plane of the major surface 2002. Moreover, therisers 2305 extend substantially perpendicular to the flats 2304.

In accordance with an embodiment, the step features 2301 of the concave,stepped surface, can include flats 2304 defining a particular averagewidth relative to the length (l) of the body 2001. For example, theflats 2304 can have an average width (wf) that is not greater than about0.8(l), wherein “l” defines the length or longest dimension of the body2001 (see. FIG. 21) extending along one side of the major surface 2002.In another embodiment, the flats 2304 can have an average width (wt)that can be not greater than about 0.5(l), such as not greater thanabout 0.4(l), not greater than about 0.3(l), not greater than about0.2(l), not greater than about 0.1(l), not greater than about 0.09(l),not greater than about 0.08(l). In still one non-limiting embodiment,the flats 2304 can have an average width (wf) that can be at least about0.001(l), such as at least about 0.005(l), at least about 0.01(l). Itwill be appreciated that the flats 2304 can have an average width (wf)within a range between any of the minimum and maximum values notedabove, including for example, within a range including at least about0.001(l) and not greater than about 0.8(l), such as at least about0.005(l) and not greater than about 0.4(l), or even at least about0.01(l) and not greater than about 0.2(l).

In another embodiment, the risers 2305 can have an average height (hr)extending in a direction substantially perpendicular to the plane of themajor surface 2002 that can be formed to have a particular relationshipto the length (l) of the body 2001 of the shaped abrasive particle 2000.For example, the average height (hr) of the risers can be not greatabout 0.2(l), wherein “l” defines the length of the body 2001. Inanother embodiment, the risers 2305 can have an average height (hr) notgreater than about 0.15(l), such as not greater than about 0.1(l), notgreater than about 0.05(l), or even not greater than about 0.02(l). Inat least one non-limiting embodiment, the risers 2305 can have anaverage height (hr) of at least about 0.0001(l), such as at least about0.0005(l). It will be appreciated that the risers 2305 can have anaverage height (hr) that is within a range including any of the minimumand maximum values noted above, including for example, at least about0.0001(l) and not greater than about 0.2(l), or at least about 0.0005(l)and not greater than about 0.1(l).

Still another embodiment, the step features 2301 including the flats2304 and risers 2305 may be formed to have a certain relationshiprelative to each other that may facilitate improved performance of theshaped abrasive particle and associated abrasive article. For example,the flats 2304 may have a particular average width (wr) that is greaterthan the average height (hr) of the risers 2305. In more particularinstances, the average height (hr) of the risers 2305 can be not greaterthan about 0.95(wf). According to another embodiment, the average height(hr) of the risers 2305 can be not greater than about 0.9(wf), such asnot greater than about 0.8(wf), not greater than about 0.7(wf), notgreater than about 0.5(wf), not greater than about 0.3(wf), not greaterthan about 0.2(wf), not greater than about 0.1(wf). In one non-limitingembodiment, the average height (hr) of the risers 2305 can be at leastabout 0.0001(wf), such as at least about 0.001(wf). It will beappreciated that the average height (hr) of the risers 2305 can bewithin a range including any of the minimum and maximum values notedabove, including for example, at least about 0.0001(wf) and not greaterthan about 0.95(wf), or even at least about 0.001(wf) and not greaterthan about 0.2(wf).

Formation of the concave, stepped surface including step features 2301can be facilitated by control of the filling pattern used to form theupper surface 2002 of the body 2001. It will be appreciated that inother instances, alternative filling patterns may be used to formalternative features in one or more major surfaces of the body 2001. Forexample, in one embodiment the upper surface for at least one majorsurface of the body 2001 can have a convex, stepped surface. A convex,stepped surface may have a thickness at a midpoint 2302 that is greaterthan a thickness of the body at an edge. As such, such a convex, steppedsurface may include stepped features, wherein the thickness of the bodydecreases moving from the midpoint 2302 to the edge 2303. Such a featuremay be facilitated by formation of the upper surface utilizing aparticular filling pattern, including for example, an inside-out fillingprocess, wherein the material at the midpoint 2302 is deposited beforethe material at the edge 2303.

In another embodiment, certain shaped abrasive particles formedaccording to the methods described herein can include a body that has atleast one peripheral ridge extending around at least a portion of a sidesurface of the body. FIG. 24 includes a side view image of a portion ofa shaped abrasive particle according to an embodiment. As provided, theshaped abrasive particle 2400 can include a body 2401 including a firstmajor surface 2402, a second major surface 2403 opposite the first majorsurface 2402, and side surfaces 2404 and 2405 extending between thefirst major surface 2402 and second major surface 2403. As furtherillustrated, the side surfaces 2404 and 2405 can include at least oneperipheral ridge 2407 extending around at least a portion of the sidesurfaces 2404 and 2405 of the body 2401. In certain instances, the oneor more peripheral ridges 2407 can extend around the majority of theside surfaces 2404 and 2405 of the body 2401. For certain embodiments,the one or more peripheral ridges 2407 can extend around the entireperipheral length of the side surfaces 2404 and 2405 of the body 2401.As further illustrated, the at least one peripheral ridge 2407 canextend in a direction generally perpendicular to the thickness (t) ofthe body and substantially parallel to the planes defined by the firstmajor surface 2402 and second major surface 2403.

Furthermore, in at least another embodiment at least one of theperipheral ridges 2407 can extend around the entire side surface of thebody 2401 without intersecting one or more major surfaces, including forexample, the first major surface 2402 and/or the second major surface2403. As illustrated in FIG. 24, at least one of the peripheral ridges2407 can extend along at least two side surfaces 2404 and 2405 and anadjoining edge 2408 extending between the side surfaces 2404 and 2405.

For certain shaped abrasive particles of the embodiments herein, theperipheral ridges 2407 can be separated by protrusions 2406. Inparticular, each pair of peripheral ridges 2407 can be separated by atleast one protrusion of the group of protrusions 2406. Notably, theprotrusions 2406 can each have a thickness that is less than the totalthickness (t) of the body 2401.

In one embodiment, the at least one peripheral ridge 2407 can have adepth (dr) that extends from an upper surface into the body and having aparticular relationship relative to the thickness (t) of the body 2401.For example, the at least one peripheral ridge 2407 can have a depth(dr) that is not greater than about 0.8(t), wherein “t” is a thicknessof the body. Still, the at least one peripheral ridge 2407 can have adepth (dr) that is not greater than about 0.7(t), such as not greaterthan about 0.6(t), not greater than about 0.5(t), not greater than about0.4(t), not greater than about 0.3(t), not greater than about 0.2(t),not greater than about 0.18(t), not greater than about 0.16(t), notgreater than about 0.15(t), not greater than about 0.14(t), not greaterthan about 0.12(t), not greater than about 0.1(t), not greater thanabout 0.09(t), not greater than about 0.08(t), not greater than about0.07(t), not greater than about 0.06(t), or even not greater than about0.05(t). In one non-limiting embodiment, the at least one peripheralridge 2407 can have a depth (dr) that is at least about 0.001(t), suchas at least about 0.01(t). It will be appreciated that the depth (dr) ofthe at least one peripheral ridge 2407 can be within a range includingany of the minimum and maximum values noted above, including for examplea depth (dr) of at least about 0.001(t) and not greater than about0.8(t), such as at least about 0.001(t) and not greater than about0.5(t), or even at least about 0.001(t) and not greater than about0.1(t). Furthermore, it will be appreciated that reference herein to theat least one peripheral ridge having a depth (dr) can also refer to anaverage depth of the plurality of peripheral ridges 2407. Moreover, theaverage depth of the plurality of peripheral ridges 2407 can have thesame relationship relative to the average thickness (t) of the body 2401as described above.

At least one embodiment, shaped abrasive particles of the embodimentsherein can include at least one transverse ridge that can extend over atleast two surfaces and an adjoining edge between the at least twosurfaces. Referring again to FIG. 24, the at least one peripheral ridge2407 can be in the form of a transverse ridge that extends over thefirst side surface 2404, second side surface 2405, and the adjoiningedge 2408 between the first side surface 2404 and the second sidesurface 2405. In more particular instances, a transverse ridge canextend over at least three surfaces in at least two adjoining edgesbetween the at least three surfaces. For example, in the instance of ashaped abrasive particle having a triangular two-dimensional shape asviewed top-down, a transverse ridge can extend around the side surfacesbetween the major surfaces such that the transverse ridge extends overall three sides surfaces and at least two of the adjoining edges betweenthe at least three surfaces. It will be appreciated that the transverseridges can extend around the entire periphery of the side surfaces ofthe body, which may include more than three side surfaces in the case ofa body having other two-dimensional shapes as viewed top down (e.g., arectangular two-dimensional shape with four side surfaces and fouradjoining edges).

In another embodiment, the body of the shaped abrasive particle caninclude a plurality of transverse ridges 2407, wherein each of thetransverse ridges of the plurality of transverse ridges 2407 extendparallel to each other around at least a portion of the periphery of thebody 2401. In another embodiment, at least one of the transverse ridgesof the plurality of transverse ridges can have a different lengthrelative to each other. It will be appreciated that the length is ameasure of the longest dimension of the transverse ridge. For example,in the embodiment of FIG. 24, the transverse ridges 2407 can havelengths extending perpendicular to the thickness “t” of the body 2401.However, it will be appreciated that some of the transverse ridges 2407may have lengths that differ from others, such that at least one of thetransverse ridges 2407 has a length that is greater than or less than alength of another transverse ridge. According to a particularembodiment, each of the transverse ridges 2407 of the pluralitytransverse ridges can have different lengths relative to each other.

In yet another aspect, the shaped abrasive particles of the embodimentsherein may include a body having at least one corner that includes aplurality of micro-protrusions extending from the corner. The formationof a body having at least one corner with the micro-protrusions mayfacilitate improved abrasive performance. FIG. 25 includes an image of aportion of a corner of a shaped abrasive particle according to anembodiment herein. The shaped abrasive particle 2500 can include a body2501 having a corner 2502 that can include a plurality ofmicro-protrusions 2503 extending from the corner 2502. In accordancewith an embodiment, the micro-protrusions 2503 can define a plurality ofdiscrete corner protrusions 2504, 2505, 2506, and 2507 (2504-2507)separated by a plurality of ridges 2508. In accordance with oneembodiment, the plurality of discrete corner protrusions 2504-24 507 canhave different shapes relative to each other. For example, the discreteprotrusion 2504 is extending further in a lateral direction from thecorner 2502 relative to the discrete corner protrusion 2505.

Furthermore, the discrete corner protrusion 2504-2507 can have differentcorner contours relative to each other. For example, the discrete cornerprotrusion 2504 as viewed top-down can have a sharper corner roundnessrelative to the other discrete corner protrusion 2505, 2506 and 2507. Incertain instances, each of the discrete corner protrusions 2504-2507 canhave different corner roundness values relative to each other. In yetanother embodiment, the micro-protrusions 2503 associate with the corner2502 can define a plurality of discrete corner protrusion 2504 and 2507,which may have different contours relative to each other. In oneparticular embodiment, the corner 2502 can have a different cornerroundness values at the upper surface 2510 defined by the discretecorner protrusion 2507 relative to the average corner roundness of thecorner at the bottom surface 2511 defined by the discrete cornerprotrusion 2504.

In another embodiment, the particular feature of the micro-protrusions2503 can include a plurality of discrete corner protrusions 2504-2507,wherein at least two of the discrete corner protrusions can define astep having a lateral shift relative to each other. For example, thediscrete corner protrusion 2504 can extend further from the body 2501relative to the discrete corner protrusion 2505 and define a lateralshift 2509 between the outermost peripheral edge of the discrete cornerprotrusion 2504 relative to the outermost peripheral edge of thediscrete corner protrusion 2505.

In accordance with another embodiment, the corner 2502 including themicro-protrusions 2503 can define a serrated edge in accordance with oneembodiment. The micro-protrusions 2503 can define a serrated contouralong the edge 2513 extending between the first major surface 2510 andthe second major surface 2511. More particularly, the formation ofdiscrete corner protrusions 2504-1507 separated by ridges 2508 can givethe edge 2513 a serrated contour that may facilitate improved abrasivecapabilities.

In yet another aspect, the shaped abrasive particles of the embodimentsherein can include a body having a scalloped topography defining aplurality of curved protrusions having ridges extending between thecurve protrusions. In a one embodiment, FIG. 26 includes an image of aportion of a surface of a shaped abrasive particle having a scallopedtopography. As illustrated, the body 2601 can include a portionincluding a scalloped topography 2602. The scalloped topography 2602 caninclude a plurality of curved protrusions 2603 having ridges 2604extending between the curve protrusions 2603. In accordance with oneembodiment, the scalloped topography 2602 can extend over a majority ofan entire surface of the body 2601. In certain instances, the scallopedtopography 2602 can extend over an entire surface of one surface (e.g.,side surface or major surface) of the body of the shaped abrasiveparticle. In yet another design, the scalloped topography 2602 canextend over a majority of the entire side surface area of the body 2601of the shaped abrasive particle. Still in at least one embodiment, thescalloped topography 2602 can extend over the entire surface area of thebody 2601 of the shaped abrasive particle.

The scalloped topography 2602 can include curve protrusions 2603defining arcuate portions of the external surface of the body extendingbetween ridges 2604. In one particular embodiment, the curve protrusions2603 can be in the form of each elongated protrusions, wherein eachprotrusion has a length (l), width (w), and a height (h), wherein eachprotrusion can have an arcuate contour in the direction of the width andthe height. For example, as illustrated in the embodiment of FIG. 26,the curve protrusions 2603 can be an elongated protrusion 2605 having alength 2606, a width of 2607, and a height 2608. As will be appreciatedthe length 2606 can define the longest dimension of the elongatedprotrusion 2605, the width 2607 can extend in a direction substantiallyperpendicular to the length 2606, and in particular, can extend for thedistance between adjacent ridges on either side of the elongatedprotrusion 2605. The elongated protrusion 2605 can further include aheight 2608 that can define the greatest distance the elongatedprotrusion 2605 extends in a direction perpendicular to the planedefined by the length 2606 and width 2607. The height 2608 may furtherbe defined the distance between the highest point on the elongatedprotrusion 2605 and lowest point, which may be associated with a ridgeadjacent either side of the elongated protrusion 2605.

In at least one embodiment, the elongated protrusion 2605 can have alength 2606 extending in substantially the same direction as the lengthof the body 2601 of the shaped abrasive particle. In accordance with oneembodiment the length of at least one elongated protrusion 2605 can beat least about 0.8(l) where “l” is the length of the body 2601 of theshaped abrasive particle. In other instances, the length of theelongated protrusion 2605 can be at least 0.9(l), or even at least about1(l), such that the length of the elongated protrusion 2605 isequivalent to the length of the body 2601. It will be appreciated thatreference to the length of the elongated protrusion 2605 can includereference to an average length of a plurality of elongated protrusions,and the average length can have the same relationship relative to thelength of the body as described above.

The elongated protrusions can be formed to have a particularrelationship of width 2607 relative to the height 2608. For example, onone or more of the plurality of elongated protrusions, including forexample, the elongated protrusion 2605 can have a height 2608 that isless than the width 2607. It will be appreciated that the body 2601 caninclude a plurality of elongated protrusion, which can define an averagewidth and average height, and reference herein to a width or height canalso include reference to an average width or average height for aplurality of elongated protrusions. The average height (hep) of theplurality of elongated protrusions 2603 can be not greater than about0.9(wep), wherein “wep” represents the average width of the elongatedprotrusions, such as not greater than about 0.8(wep), not greater thanabout 0.7(wep), not greater than about 0.6(wep), not greater than about0.5(wep), not greater than about 0.4(wep), not greater than about0.3(wep), not greater than about 0.2(wep), or even not greater thanabout 0.1(wep). Still, in at least one embodiment, the plurality ofelongated protrusions can have an average height (hep) that is at leastabout 0.001(wep), or even at least about 0.1(wep). It will beappreciated that the average height (hep) of the plurality of elongatedprotrusions can be within a range including any of the minimum andmaximum values above, including for example, at least about 0.001(wep)and not greater than about 0.9(wep), or at least about 0.001(wep) andnot greater than about 0.5(wep).

In accordance with one embodiment, the average height of the pluralityof elongated protrusions 2603 can be not greater than about 500 microns,such as not greater than about 400 microns, not greater than about 300microns, not greater than about 250 microns, not greater than about 200microns, not greater than about 150 microns, not greater than about 100microns, not greater than about 90 microns, not greater than about 30microns, or even not greater than about 50 microns. Still, in onenon-limiting embodiment, the average height of the plurality ofelongated protrusions 2603 can be at least about 0.01 microns, at leastabout 0.1 microns, or even at least about 1 micron. It will beappreciated that the average height of the plurality of elongatedprotrusions 2603 can be within range including any of the minimum andmaximum values noted above, including for example, at least about 0.1microns and not great than about 200 microns, such as at least about 0.1microns and not than about 100 microns.

In accordance with another embodiment, the plurality of elongatedprotrusions 2603 can have an average width that is less than the averagelength of the body. In certain instances, the plurality of elongatedprotrusions may have a particular relationship to the average widthrelative to the length of the body 2601 of the shaped abrasive particle.For example, the average width of the plurality of elongated protrusionscan be not greater than about 0.9(l), such as not greater than about0.8(l), not greater than about 0.7(l), not greater than about 0.6(l),not greater than about 0.5(l), not greater than about 0.4(l), notgreater than about 0.3(l), not greater than about 0.2(l), or even notgreater than about 0.1(l). Still, in at least one non-limitingembodiment, the average width of the plurality of elongate protrusionscan be at least 0.001(l), or at least the 0.01(l). It will beappreciated that the average width can be within range including any ofthe minimum and maximum values noted above, including for example, atleast about 0.001(l) and not greater than about 0.9(l), such as at leastabout 0.01(l) and not great than about 0.5(l).

In certain instances, the plurality of elongated protrusions can have anaverage width that is not greater than about 500 microns, such notgreater than about 400 microns, not greater than about 300 microns, notgreater than about 250 microns, or even not greater than about 200microns. Still, in at least one non-limiting embodiment, the averagewidth of the plurality of elongate protrusions can be at least about0.01 microns, at least about 0.1 microns, or even at least about 1micron. It will be appreciated that the plurality of elongatedprotrusions can have an average width within a range including any ofthe minimum and maximum values noted above, including for example, atleast about 0.01 microns and not greater than about 500 microns, such asat least about 0.01 microns and not greater than about 300 microns.

As further illustrated in FIG. 26, the scalloped topography 2602 mayfacilitate formation of sides and edges of the shaped abrasive particlehaving a non-linear feature which may beneficially affect the abrasiveproperties of the shaped abrasive particles. For example, the scallopedtopography may facilitate improved fracture mechanics of the shapedabrasive particle. In at least one particular embodiment, scallopedtopography 2602 can intersect an edge defining at least one corner ofthe body. For example, referring again to FIG. 25, the side surface 2514between the major surfaces 2510 and 2511 can have a scalloped topographythat intersects the corner 2502 and defines a serrated contour along thelength of the edge 2513. Formation of a serrated edge 2513 mayfacilitate improved abrasive capabilities of the shaped abrasiveparticle.

In accordance with an embodiment, the body of the shaped abrasiveparticle can include at least four major surfaces joined together atcommon edges. In certain instances, the four major surfaces can havesubstantially the same surface area relative to each other. Morespecifically, the body may include a tetrahedral shape.

FIG. 27 includes a top-down image of a shaped abrasive particleaccording to the embodiment. FIG. 27 includes a shaped abrasive particleincluding a bottom surface 2702, three major side surfaces 2703, 2704,and 2705 joined to the bottom surface 2702 along common edges defined bythe peripheral surface of the bottom surface 2702. As further providedin FIG. 27, the body 2701 of the shaped abrasive particle includes anupper surface 2706. The upper surface 2706 can include a peripheralsurface 2708 having a generally planar contour. Accordingly, the body2701 can represent a truncated tetrahedral shaped abrasive particle, andmore specifically, a volcano shape shaped abrasive particle.

The body 2701 can include an opening 2709, which may be in the form of ablind opening or depression extending into the body at the upper surface2706. In one particular embodiment, the upper surface 2706 can have aconcave, stepped surface defined by the peripheral surface 2708 and afirst stepped surface 2711 having a substantially planar region (e.g., aflat) in the form of a triangular area. The first stepped surface 2711can define a step disposed in the opening 2709. The first steppedsurface 2711 can be recessed into the opening 2709 below the peripheralsurface 2708. The concave, stepped surface can also include a secondstepped surface 2712 having a substantially planar region, which may bein the form of a triangular area, and recessed into the opening 2709below the planar peripheral surface 2708 and the first stepped surface2711. The concave, stepped surface can also include a riser 2713 betweenthe first stepped surface 2711 and the peripheral surface 2708. Theconcave, stepped surface may also include a riser 2714 between thesecond stepped surface 2712 and the first stepped surface 2713. Inparticular embodiments having an opening 2709 in the upper surface 2706,the shaped abrasive particle may define a volcano shape shaped abrasiveparticle, wherein the midpoint 2710 of the opening 2709 is recessed intothe body away from the planar peripheral surface 2708.

As also provided in FIG. 27, the body 2701 can be formed of a pluralityof portions, including for example, portion 2721 defining the peripheralsurface of the bottom surface 2702 and portion 2722 overlying the firstportion 2721. The body can further include a plurality of overlyingportions above the portions 2721 and 2722. As illustrated, the portions2721 and 2722 can be in the form of triangular layers as viewed top-downin FIG. 27. Moreover, as illustrated, the layers can facilitate theformation of edges 2731, 2732, and 2733 between the major surface 2703,2704, and 2705 and extending from the upper surface 2707 to the bottomsurface 2702 having micro-protrusions. The micro-protrusions can definea serrated contour along the edges 2731, 2732, and 2733.

Moreover, the major surfaces 2703, 2704, and 2705 can have a pluralityof elongated protrusions 2741 extending around the periphery of thesurfaces. The body 2701 can also include a plurality transverse ridges2742 extending around the major surfaces 2703, 2704, and 2705 andadjoining edges 2731, 2732, and 2733. Looking top-down as provided inFIG. 27, the major surfaces 2703, 2704, and 2705 can also have ascalloped topography defining a plurality of arcuate protrusions 241separated by the plurality of transverse ridges 2742.

FIG. 28 includes a top-down view of a shaped abrasive particle accordingto an embodiment. As provided, the body 2801 of the shaped abrasiveparticle can include a bottom surface 2802 and major side surfaces 28032804, and 2805 joined to the bottom surface 2802 at the peripheralsurface 2806 of the bottom surface 2802. The body 2801 can furtherinclude corners 2811, 2812, 2813, and 2814 joined by the edges 2821,2822, and 2823 such that the body forms a tetrahedral shape. Unlike theshaped abrasive particle of FIG. 27, the body 2801 of the shapedabrasive particle of FIG. 28 is not a truncated pyramid, but includesthe four corners 2811, 2812, 2813, and 2814. Notably, the corners 2811,2812, and 2813 can be defined by a first portion 2831 of the body andthe corner 2814 can be defined by a second portion 2832 formed at asecond time and distinct from the portion 2831. In at least oneembodiment, the corners 2811, 2812, and 2813 can have substantially thesame corner roundness value and the corner 2814 can have a cornerroundness value that is different than the corner roundness values ofthe corners 2811, 2812, and 2813. In at least one embodiment, the corner2814 can have a corner roundness value that is greater than the cornerroundness values of the corners 2811, 2812, and 2813. In still anotherembodiment, the corner 2814 can have a corner roundness value that isless than the corner roundness values of the corners 2811, 2812, and2813. FIG. 29 includes a side-view image of the shaped abrasive particleof FIG. 28. It will be appreciated that the shaped abrasive bodyparticles of the embodiments herein can include bodies having variousthree-dimensional shapes as described herein, and are not to beinterpreted as limited to those embodiments illustrated or depicted.

Without wishing to be tied to a particular theory, it is thought thatone or more features of the embodiments herein can facilitate formationof shaped abrasive particles having improved abrasive properties. Incertain instances, it has been noted that the shaped abrasive particlescan have unique fracturing behavior, wherein during abrasive operationsregions of the portions making up the body of the shaped abrasiveparticle may be selectively removed, which may expose sharper portions,thus exhibiting a self-sharpening behavior. FIG. 30 includes an image ofa corner of a shaped abrasive particle according to an embodiment. Asprovided, certain region 3002 of a portion 3003 of the body 3001 of theshaped abrasive particle have been removed during an abrasive operationto expose an unused region 3005 of another portion 3006 of the body3001, which has a sharp corner and may facilitate continued abrasiveoperations.

Items

Item 1. A method of forming a shaped abrasive particle having a bodyformed by an additive manufacturing process.

Item 2. A method comprising forming a body of a shaped abrasive particleaccording to a digital model.

Item 3. The method of any one of items 1 and 2, wherein the additivemanufacturing process includes forming a body of a shaped abrasiveparticle by shaping a raw material without use of a production tool.

Item 4. The method of any one of items 1 and 2, wherein the additivemanufacturing process includes forming a body of a shaped abrasiveparticle by depositing a plurality of discrete portions in a controlled,non-random manner relative to each other.

Item 5. The method of item 4, wherein depositing a plurality of portionsof the body in a controlled, non-random manner relative to each otherincludes deposition of the plurality of portions into a production tool.

Item 6. The method of any one of items 1 and 2, wherein the methodcomprises at least one process selected from the group consisting oflayer additive method, light photopolymerization, laser powder forming,powder bed fusion, selective laser sintering, micro-laser sintering,material extrusion robocasting, material jetting, sheet lamination, anda combination thereof.

Item 7. The method of item 6, wherein light photopolymerization includesstereolithography, wherein stereolithography includes depositing atleast one layer of a slurry containing a polymer material that ispolymerized during the forming process to form a shaped abrasiveparticle.

Item 8. The method of item 6, wherein laser powder forming includesdepositing a raw material on a target and impinging radiation from alaser source on the target to melt the raw material and form the rawmaterial into a shaped abrasive particle.

Item 9. The method of item 8, wherein the shaped abrasive particlecomprises a material selected from the group consisting of a metal,metal alloy, glass, ceramic, polymer, and a combination thereof.

Item 10. The method of item 9, wherein the shaped abrasive particleconsists essentially of a glass material comprising an oxide.

Item 11. The method of item 6, wherein selective laser sinteringincludes impinging radiation from a laser source on a target including araw material and changing at least a portion of one of the phases of theraw material into a shaped abrasive particle.

Item 12. The method of item 11, wherein selective laser sinteringincludes impinging radiation from a laser source on a select portion ofa bed of raw material and converting a portion of the bed of rawmaterial into a shaped abrasive particle.

Item 13. The method of item 11, wherein changing at least a portion ofone of the phases of the raw material includes a change in crystallinestructure of the raw material.

Item 14. The method of item 11, wherein changing at least a portion ofone of the phases of the raw material includes a change from a solidphase to a liquid phase of the raw material.

Item 15. The method of item 11, wherein changing at least a portion ofone of the phases of the raw material includes sintering of the rawmaterial.

Item 16. The method of item 11, wherein the shaped abrasive particlecomprises a material selected from the group consisting of a metal,metal alloy, glass, ceramic, polymer and a combination thereof.

Item 17. The method of item 6, wherein material jetting includesdeposition of discrete droplets of raw material on a target andcoalescence of the discrete droplets into a body to form a shapedabrasive particle.

Item 18. The method of item 6, wherein material jetting includesdepositing a plurality of discrete droplets into production tool in acontrolled, non-random arrangement to form a shaped abrasive particle.

Item 19. The method of any one of items 1 and 2, wherein forming thebody comprises controlling at least one process parameter selected fromthe group consisting of: a nozzle tip length; a nozzle width; a nozzleaspect ratio; a deposition pressure; a relationship between nozzle widthand deposition pressure; a deposition rate; a deposition volume, arelationship between deposition rate and deposition position; arelationship between deposition pressure and deposition position; ashutoff distance; a premove delay; a dispense gap; a filling pattern ofthe print material; a dynamic yield stress (σd) of a print material; astatic yield stress (σs) of a print material; a yield stress ratio(σd/σs) of a print material; a viscosity of the print material; and acombination thereof.

Item 20. The method of item 19, further comprising: depositing a firstprint material as a first portion of the body at a first time; anddepositing a second print material as a second portion of the bodydistinct from the first portion at a second time.

Item 21. The method of item 20, wherein the first print material has afirst composition and the second print material comprises a secondcomposition.

Item 22. The method of item 21, wherein the first composition and thesecond composition are significantly different compared to each other.

Item 23. The method of item 21, wherein the second composition has adifference in porosity relative to the first composition.

Item 24. The method of item 21, wherein the first print material andsecond print material are deposited at different regions within the bodyand configured to affect the fracturing behavior of the shaped abrasiveparticle.

Item 25. The method of item 21, wherein the first print material andsecond print material are deposited in alternative layers within aregion of the body forming a composite material configured to control aself-sharpening behavior of the body.

Item 26. The method of item 21, wherein the first print material andsecond print material are deposited in different regions of the bodyforming a composite material including a controlled arrangement of theregions relative to an intended orientation of the shaped abrasiveparticle in a fixed abrasive article.

Item 27. The method of item 20, wherein depositing the first printmaterial comprises forming a first layer of the body at a first time anddepositing the second print material comprises forming a second layer ofthe body overlying the first layer.

Item 28. The method of item 20, wherein the first portion can have afirst characteristic selected from the group consisting of hardness,porosity, composition, and a combination thereof, and the second portioncan have a second characteristic selected from the group consisting ofhardness, porosity, composition, and a combination thereof, and whereinthe first characteristic can be different from the secondcharacteristic.

Item 29. The method of item 28, wherein the first portion can have afirst porosity that is greater than a second porosity of the secondportion, and wherein the first portion and the second portion aredeposited in an arrangement relative to each other within the bodyforming a composite material configured to affect the fracturingbehavior of the shaped abrasive particle.

Item 30. The method of item 28, wherein the first portion can have afirst hardness that is greater than a second hardness of the secondportion, and wherein the first portion and the second portion aredeposited in an arrangement relative to each other within the bodyforming a composite material configured to affect the fracturingbehavior of the shaped abrasive particle.

Item 31. The method of item 20, wherein the first portion can have afirst volume that is greater than a second volume of the second portion.

Item 32. The method of item 31, wherein the first portion can define acentral region of the body and the second portion can define an edge ofthe body.

Item 33. The method of item 31, wherein the first portion can define acentral region of the body and the second portion can define a corner ofthe body.

Item 34. The method of item 19, wherein the method of forming the bodyfurther comprises depositing a print material from a nozzle onto asubstrate, wherein the movement of the nozzle is controlled by acomputer program.

Item 35. The method of item 34, wherein the nozzle comprises a nozzlewidth not greater than about 200 microns or not greater than about 100microns or not greater than about 90 microns or not greater than about85 microns or not greater than about 80 microns or not greater thanabout 75 microns or not greater than about 70 microns or not greaterthan about 65 microns or not greater than about 60 microns or notgreater than about 55 microns or not greater than about 50 microns ornot greater than about 45 microns or not greater than about 40 micronsor not greater than about 35 microns or not greater than about 30microns or not greater than about 25 microns or not greater than about20 microns.

Item 36. The method of item 34, wherein the nozzle comprises a width ofat least about 0.1 microns or at least about 1 micron or at least about10 microns.

Item 37. The method of item 19, wherein the nozzle comprises a tiplength of not greater than about 10 mm or not greater than about 8 mm ornot greater than about 6 mm or not greater than about 5 mm or notgreater than about 4 mm.

Item 38. The method of item 19, wherein the nozzle comprises a tiplength of at least about 0.1 mm or at least about 0.2 mm or at leastabout 0.5 mm or at least about 1 mm.

Item 39. The method of item 19, wherein the nozzle comprises an aspectratio value (width/tip length) of not greater than about 0.8 or notgreater than about 0.6 or not greater than about 0.5 or not greater thanabout 0.4.

Item 40. The method of item 19, wherein the nozzle comprises an aspectratio value (width/tip length) of at least about 0.001 or at least about0.005 or at least about 0.008.

Item 41. The method of item 19, wherein the deposition pressure is notgreater than about 5 MPa or not greater than about 4.5 MPa or notgreater than about 4 MPa or not greater than about 3.5 MPa or notgreater than about 3 MPa or not greater than about 2.5 MPa or notgreater than about 2 MPa or not greater than about 1.8 MPa or notgreater than about 1.5 MPa or not greater than about 1.3 MPa or notgreater than about 1 MPa or not greater than about 0.9 MPa or notgreater than about 0.8 MPa or not greater than about 0.7 MPa.

Item 42. The method of item 19, wherein the deposition pressure is atleast about 0.005 MPa or at least about 0.01 MPa or at least about 0.05MPa or at least about 0.08 MPa or at least about 0.1 MPa.

Item 43. The method of item 19, wherein the relationship between nozzlewidth and deposition pressure (width/pressure) defines a first formingfactor having a value of at least about 0.2 microns/MPa or at leastabout 1 micron/MPa or at least about 2 microns/MPa or at least about 4microns/MPa or at least about 6 microns/MPa or at least about 8microns/MPa or at least about 10 microns/MPa or at least about 12microns/MPa or at least about 14 microns/MPa or at least about 16microns/MPa.

Item 44. The method of item 19, wherein the relationship between nozzlewidth and deposition pressure (width/pressure) defines a first formingfactor having a value of not greater than about 1×10⁵ microns/MPa or notgreater than about 1×10⁴ microns/MPa or not greater than about 8000microns/MPa or not greater than about 6000 microns/MPa or not greaterthan about 5000 microns/MPa or not greater than about 4000 microns/MPaor not greater than about 3000 microns/MPa or not greater than about2000 microns/MPa or not greater than about 1000 microns/MPa or notgreater than about 500 microns/MPa or not greater than about 200microns/MPa or not greater than about 100 microns/MPa.

Item 45. The method of item 19, wherein forming comprises moving thenozzle at a deposition rate of at least about 0.01 mm/s or at leastabout 0.05 mm/s or, at least about 0.08 mm/s or at least about 0.1 mm/sor at least about 0.3 mm/s or at least about 0.5 mm/s or at least about0.8 mm/s or at least about 1 mm/s or at least about 1.5 mm/s or at leastabout 2 mm/s or at least about 2.5 mm/s or at least about 3 mm/s.

Item 46. The method of item 19, wherein forming comprises moving thenozzle at a deposition rate of not greater than about 50 mm/s or notgreater than about 30 mm/s or not greater than about 20 mm/s.

Item 47. The method of item 19, wherein forming comprises controlling adeposition volume of a print material to define a portion of the body.

Item 48. The method of item 47, wherein controlling the depositionvolume comprises changing the deposition volume of the print materialdepending upon the portion of the body being formed.

Item 49. The method of item 47, wherein forming comprises depositing asmaller volume of material at a region defining a corner of the body ascompared to a region defining a major surface of the body.

Item 50. The method of item 47, wherein controlling the depositionvolume includes controlling a deposition pressure and deposition rate ofthe nozzle.

Item 51. The method of item 50, wherein controlling the depositionvolume includes controlling a width, length, and height of a firstportion of the body formed at a first time.

Item 52. The method of item 19, wherein forming comprises controllingthe relationship between deposition rate and deposition position.

Item 53. The method of item 52, wherein controlling the relationshipbetween deposition rate and deposition positing includes changing thedeposition rate depending upon the deposition position.

Item 54. The method of item 52, wherein controlling the relationshipbetween deposition rate and deposition position includes decreasing thedeposition rate at a deposition position associated with a corner of thebody of the shaped abrasive particle relative to a deposition rateassociated with a deposition position at a major surface of the body.

Item 55. The method of item 52, wherein controlling the relationshipbetween deposition rate and deposition position includes varying thedeposition rate to change the size of features in the body depending onthe deposition position.

Item 56. The method of item 19, wherein forming comprises controllingthe relationship between the deposition pressure and the depositionposition.

Item 57. The method of item 56, wherein controlling the relationshipbetween the deposition pressure and the deposition position includeschanging the deposition pressure depending upon the deposition position.

Item 58. The method of item 56, wherein controlling the relationshipbetween the deposition pressure and the deposition position includesdecreasing the deposition pressure at a deposition position associatedwith a corner of the body of the shaped abrasive particle relative to adeposition pressure associated with a deposition position at a majorsurface of the body.

Item 59. The method of item 56, wherein controlling the relationshipbetween the deposition pressure and the deposition position includesvarying the deposition pressure to change the size of features in thebody depending on the deposition position.

Item 60. The method of item 19, wherein forming a body further comprisescontrolling a premove delay between a beginning of deposition of theprint material and movement of a nozzle for depositing the printmaterial.

Item 61. The method of item 60, wherein the premove delay is greaterthan 0 seconds.

Item 62. The method of item 60, wherein the premove delay is not greaterthan about 10 seconds.

Item 63. The method of item 19, wherein forming a body further comprisescontrolling a shutoff distance defining the distance a nozzle movesafter turning the pressure off to the print material.

Item 64. The method of item 19, wherein the shutoff distance is lessthan a dispense gap.

Item 65. The method of item 19, wherein the shutoff distance is greaterthan a dispense gap.

Item 66. The method of item 19, wherein the shutoff distance issubstantially equal to a dispense gap.

Item 67. The method of item 19, wherein forming comprises controlling adispense gap defining a distance between the nozzle and target.

Item 68. The method of item 67, wherein the dispense gap is not greaterthan about 10 W, wherein “W” represents the width of the nozzle, whereinthe dispense gap is not greater than about 9 W or not greater than about8 W or not greater than about 7 W or not greater than about 6 W or notgreater than about 5 W or not greater than about 4 W or not greater thanabout 3 W or not greater than about 2 W or not greater than about 1 W.

Item 69. The method of item 67, wherein the dispense gap is at leastabout 0.001 W, wherein “W” represents the width of the nozzle, whereinthe dispense gap is at least about 0.005 W or at least about 0.01 W orat least about 0.1 W.

Item 70. The method of item 67, wherein the dispense gap is not greaterabout 10t, wherein “t” represents the thickness of the print material,wherein the dispense gap is not greater than about 9t or not greaterthan about 8t or not greater than about 7t or not greater than about 6tor not greater than about 5t or not greater than about 4t or not greaterthan about 3t or not greater than about 2t or not greater than about 1t.

Item 71. The method of item 67, wherein the dispense gap is at leastabout 0.001t, wherein “t” represents the thickness of the printmaterial, wherein the dispense gap is at least about 0.005t or at leastabout 0.01t.

Item 72. The method of item 67, wherein controlling the dispense gapincludes varying the dispense gap such that the print material contactsthe target immediately upon exiting the nozzle.

Item 73. The method of item 67, wherein controlling the dispense gapincludes controlling the height of the nozzle above the target such thatthe print material contacts the target upon exiting the nozzle withoutforming a free droplet in the space between the nozzle and target.

Item 74. The method of item 67, wherein controlling the dispense gapincludes varying the Z-directional distance between the nozzle and thetarget based upon at least one of the nozzle tip length, the nozzlewidth, the deposition pressure, the deposition rate, the depositionvolume, the deposition position, the filling pattern of the printmaterial, the dynamic yield stress (σd) of the print material, thestatic yield stress (σs) of the print material, the yield stress ratio(σd/σs) of the print material, the viscosity of the print material, anda combination thereof.

Item 75. The method of item 67, wherein controlling the dispense gapincludes varying the dispense gap based on the deposition position.

Item 76. The method of item 67, wherein controlling the dispense gapincludes varying the dispense gap to alter the volume of materialdeposited at a deposition position.

Item 77. The method of item 19, wherein forming further comprisescontrolling the filling pattern that defines the order of forming afirst portion of the body at a first time and a second portion of thebody at a second time.

Item 78. The method of item 77, wherein the filling pattern defines andeposition process selected from the group consisting of an outside-infilling process, an inside-out filling process, a side-to-side fillingprocess, bottom-up filling process, and a combination thereof.

Item 79. The method of item 77, wherein controlling the filling patternincludes forming a first portion of the body at a first time using afirst filling pattern and a second portion of the body at a second timeusing a second filling pattern, wherein the first filling pattern isdifferent from the second filling pattern.

Item 80. The method of item 77, wherein the filling pattern includesforming a first layer by an outside-in filling process and a secondlayer overlying the first layer by an inside-out filling process.

Item 81. The method of item 19, wherein the print material can include amixture comprising an inorganic material in a content of at least about25 wt % for a total weight of the mixture or at least about 35 wt % orat least about 36 wt % or and not greater than about 75 wt % or notgreater than about 70 wt % or not greater than about 65 wt % or notgreater than about 55 wt % or not greater than about 45 wt % or notgreater than about 44 wt %.

Item 82. The method of item 81, wherein the mixture comprises a sol-gel.

Item 83. The method of item 81, wherein the inorganic material comprisesa ceramic.

Item 84. The method of item 81, wherein the inorganic material comprisesa material selected from the group consisting of oxides, carbides,nitrides, borides, oxycarbides, oxynitrides, oxyborides, carbon-basedmaterials, and a combination thereof.

Item 85. The method of item 81, wherein the inorganic material comprisesalumina.

Item 86. The method of item 81, wherein the inorganic material comprisesboehmite.

Item 87. The method of item 81, wherein the mixture comprises nitricacid.

Item 88. The method of item 81, wherein the mixture comprises water.

Item 89. The method of item 81, wherein the mixture comprises a dynamicyield stress (σd) of at least about 100 Pa or at least about 120 Pa orat least about 140 Pa or at least about 160 Pa or at least about 180 Paor at least about 200 Pa.

Item 90. The method of item 81, wherein the mixture comprises a dynamicyield stress (σd) of not greater than about 1500 Pa or not greater thanabout 1300 Pa or not greater than about 1200 Pa or not greater thanabout 1100 Pa or not greater than about 1000 Pa.

Item 91. The method of item 81, wherein forming comprises controlling atleast one of the dispense gap, the nozzle tip length, the nozzle width,the deposition pressure, the deposition rate, the deposition volume, thedeposition position, and the filling pattern of the print material basedon the dynamic yield stress (σd) of the print material.

Item 92. The method of item 81, wherein the mixture comprises a staticyield stress (σs) of at least about 180 Pa or at least about 200 Pa orat least about 250 Pa or at least about 300 Pa or at least about 350 Paor at least about 400 Pa or at least about 450 Pa or at least about 500Pa or at least about 550 Pa or at least about 600 Pa.

Item 93. The method of item 81, wherein the mixture comprises a staticyield stress (σs) of not greater than about 20000 Pa or not greater thanabout 18000 Pa or not greater than about 15000 Pa or not greater thanabout 5000 Pa or not greater than about 1000 Pa.

Item 94. The method of item 81, wherein the mixture comprises a staticyield stress (σs) different than the dynamic yield stress (σd).

Item 95. The method of item 81, wherein the mixture comprises a staticyield stress (σs) greater than the dynamic yield stress (σd).

Item 96. The method of item 81, wherein the mixture comprises a yieldstress ratio (σd/σs) of not greater than about 1 or not greater thanabout 0.99 or not greater than about 0.97 or not greater than about 0.95or not greater than about 0.9 or not greater than about 0.85 or notgreater than about 0.8 or not greater than about 0.75 or not greaterthan about 0.7 or not greater than about 0.65 or not greater than about0.6 or not greater than about 0.55 or not greater than about 0.5.

Item 97. The method of item 81, wherein forming comprises controlling atleast one of the dispense gap, the nozzle tip length, the nozzle width,the deposition pressure, the deposition rate, the deposition volume, thedeposition position, and the filling pattern of the print material basedon the static yield stress (σs) of the print material.

Item 98. The method of item 81, wherein the mixture comprises a yieldstress ratio (σd/σs) of at least about 0.01 or at least about 0.05 or atleast about 0.08 or at least about 0.1 or at least about 0.15 or atleast about 0.2 or at least about 0.25 or at least about 0.3 or at leastabout 0.35 or at least about 0.4 or at least about 0.45 or at leastabout 0.5.

Item 99. The method of item 81, wherein forming comprises controlling atleast one of the dispense gap, the nozzle tip length, the nozzle width,the deposition pressure, the deposition rate, the deposition volume, thedeposition position, and the filling pattern of the print material basedon the yield stress ratio (σd/σs) of the print material.

Item 100. The method of item 81, wherein the mixture is a shear thinningmaterial.

Item 101. The method of item 81, wherein the mixture comprises aviscosity of at least about 4×10³ Pa s or at least about 5×10³ Pa s orat least about 6×10³ Pa s or at least about 7×10³ Pa s or at least about7.5×10³ Pa s.

Item 102. The method of item 81, wherein the mixture comprises aviscosity of not greater than about 20×10³ Pa s or such as not greaterthan about 18×10³ Pa s or not greater than about 15×10³ Pa s or notgreater than about 12×10³ Pa s.

Item 103. The method of item 81, wherein forming comprises controllingat least one of the dispense gap, the nozzle tip length, the nozzlewidth, the deposition pressure, the deposition rate, the depositionvolume, the deposition position, and the filling pattern of the printmaterial based on the viscosity of the print material.

Item 104. The method of any one of items 1 and 2, wherein formingfurther comprises controlling a three-dimensional movement of a nozzleconfigured for deposition of a print material, wherein controlling thethree-dimensional movement includes control of the nozzle in an X-axis,a Y-axis, and a Z-axis.

Item 105. The method of any one of items 1 and 2, wherein formingfurther comprises control of a plurality of nozzles, wherein each nozzleof the plurality of nozzles can be configured to deposit a printmaterial and control of the plurality of nozzles includes control ofthree-dimensional movement of each nozzle in an X-axis, a Y-axis, and aZ-axis.

Item 106. The method of any one of items 1 and 2, further comprising:depositing a first print material as a first portion of the body at afirst time; and depositing a second print material as a second portionof the body distinct from the first portion at a second time.

Item 107. The method of item 106, wherein the first time is differentthan the second time.

Item 108. The method of item 106, wherein the first print materialcomprises a material selected from the group consisting of a solid, apowder, a solution, a mixture, a liquid, a slurry, a gel, a binder, anda combination thereof.

Item 109. The method of item 106, further comprising preferentiallymodifying one of the first portion and second portion to join the firstportion and second portion and form a subsection of the body.

Item 110. The method of item 109, wherein modifying comprises changing aphase of at least one of the first print material and the second printmaterial.

Item 111. The method of item 109, wherein modifying comprises heating atleast one of the first portion and second portion.

Item 112. The method of item 111, wherein heating comprises fusing thefirst portion to the second portion.

Item 113. The method of item 111, wherein heating comprises joining thefirst portion to the second portion.

Item 114. The method of item 111, wherein heating comprises impingingelectromagnetic radiation on at least a portion of the first portion.

Item 115. The method of item 111, wherein heating comprises impingingelectromagnetic radiation on at least a portion of the second portion.

Item 116. The method of item 106, wherein depositing comprisesdepositing a plurality of discrete droplets of a predetermined volume ofthe first print material to form the first portion.

Item 117. The method of item 106, wherein depositing comprisesdepositing a plurality of discrete droplets of a predetermined volume ofthe second print material to form the second portion.

Item 118. The method of item 106, wherein the first portion comprises afirst portion length (Lfp), a first portion width (Wfp), and a firstportion thickness (Tfp), and wherein Lfp≥Wfp, Lfp≥Tfp, and Wfp≥Tfp.

Item 119. The method of item 118, wherein the first portion comprises aprimary aspect ratio (Lfp:Wfp) of at least about 1:1 or at least about2:1 or at least about 3:1 or at least about 5:1 or at least about 10:1,and not greater than about 1000:1.

Item 120. The method of item 118, wherein the first portion comprises asecondary aspect ratio (Lfp:Tfp) of at least about 1:1 or at least about2:1 or at least about 3:1 or at least about 5:1 or at least about 10:1,and not greater than about 1000:1.

Item 121. The method of item 118, wherein the first portion comprises atertiary aspect ratio (Wfp:Tfp) of at least about 1:1 or at least about2:1 or at least about 3:1 or at least about 5:1 or at least about 10:1,and not greater than about 1000:1.

Item 122. The method of item 118, wherein at least one of the firstportion length (Lfp), the first portion width (Wfp), and the firstportion thickness (Tfp) has an average dimension of not greater thanabout 2 mm or such as not greater than about 1 mm or not greater thanabout 900 microns or not greater than about 800 microns or not greaterthan about 700 microns or not greater than about 600 microns or notgreater than about 500 microns or not greater than about 400 microns ornot greater than about 300 microns or not greater than about 200 micronsor not greater than about 150 microns or not greater than about 140microns or not greater than about 130 microns or not greater than about120 microns or not greater than about 110 microns or not greater thanabout 100 microns or not greater than about 90 microns or not greaterthan about 80 microns or not greater than about 70 microns or notgreater than about 60 microns or not greater than about 50 microns, andat least about 0.01 microns or at least about 0.1 microns or at leastabout 1 micron.

Item 123. The method of item 118, wherein the first portion comprises across-sectional shape in a plane defined by the first portion length(Lfp) and the first portion width (Wfp) selected from the groupconsisting of triangular, quadrilateral, rectangular, trapezoidal,pentagonal, hexagonal, heptagonal, octagonal, ellipsoidal, Greekalphabet characters, Latin alphabet characters, Russian alphabetcharacters, and a combination thereof.

Item 124. The method of item 118, wherein the first portion comprises across-sectional shape in a plane defined by the first portion length(Lfp) and the first portion thickness (Tfp) selected from the groupconsisting of triangular, quadrilateral, rectangular, trapezoidal,pentagonal, hexagonal, heptagonal, octagonal, ellipsoidal, Greekalphabet characters, Latin alphabet characters, Russian alphabetcharacters, and a combination thereof.

Item 125. The method of item 118, wherein the first portion is in theform of layer.

Item 126. The method of item 106, wherein the second portion comprises asecond portion length (Lsp), a second portion width (Wsp), and a secondportion thickness (Tfp), and wherein Lsp≥Wsp, Lsp≥Tsp, and Wsp≥Tsp.

Item 127. The method of item 126, wherein the second portion comprises aprimary aspect ratio (Lsp:Wsp) of at least about 1:1 or at least about2:1 or at least about 3:1 or at least about 5:1 or at least about 10:1,and not greater than about 1000:1.

Item 128. The method of item 126, wherein the second portion comprises asecondary aspect ratio (Lsp:Tsp) of at least about 1:1 or at least about2:1 or at least about 3:1 or at least about 5:1 or at least about 10:1,and not greater than about 1000:1.

Item 129. The method of item 126, wherein the second portion comprises atertiary aspect ratio (Wsp:Tsp) of at least about 1:1 or at least about2:1 or at least about 3:1 or at least about 5:1 or at least about 10:1,and not greater than about 1000:1.

Item 130. The method of item 126, wherein at least one of the secondportion length (Lsp), the second portion width (Wsp), and the secondportion thickness (Tsp) has an average dimension of not greater thanabout 2 mm or such as not greater than about 1 mm or not greater thanabout 900 microns or not greater than about 800 microns or not greaterthan about 700 microns or not greater than about 600 microns or notgreater than about 500 microns or not greater than about 400 microns ornot greater than about 300 microns or not greater than about 200 micronsor not greater than about 150 microns or not greater than about 140microns or not greater than about 130 microns or not greater than about120 microns or not greater than about 110 microns or not greater thanabout 100 microns or not greater than about 90 microns or not greaterthan about 80 microns or not greater than about 70 microns or notgreater than about 60 microns or not greater than about 50 microns, andat least about 0.01 microns or at least about 0.1 microns or at leastabout 1 micron.

Item 131. The method of item 126, wherein the second portion comprises across-sectional shape in a plane defined by the second portion length(Lsp) and the second portion width (Wsp) selected from the groupconsisting of triangular, quadrilateral, rectangular, trapezoidal,pentagonal, hexagonal, heptagonal, octagonal, ellipsoidal, Greekalphabet characters, Latin alphabet characters, Russian alphabetcharacters, and a combination thereof.

Item 132. The method of item 126, wherein the second portion comprises across-sectional shape in a plane defined by the second portion length(Lsp) and the second portion thickness (Tsp) selected from the groupconsisting of triangular, quadrilateral, rectangular, trapezoidal,pentagonal, hexagonal, heptagonal, octagonal, ellipsoidal, Greekalphabet characters, Latin alphabet characters, Russian alphabetcharacters, and a combination thereof.

Item 133. The method of item 126, wherein the first portion comprises across-sectional shape different than a cross-sectional shape of thesecond portion.

Item 134. The method of item 126, wherein the first portion comprises across-sectional shape substantially the same as a cross-sectional shapeof the second portion.

Item 135. The method of item 106, wherein the first print materialcomprises a first composition and the second print material comprises asecond composition.

Item 136. The method of item 135, wherein the first composition and thesecond composition are essentially the same with respect to each other.

Item 137. The method of item 135, wherein the first composition and thesecond composition are significantly different with respect to eachother.

Item 138. The method of item 135, wherein the first compositioncomprises a material selected from the group consisting of organicmaterial, inorganic material, and a combination thereof.

Item 139. The method of item 135, wherein the first compositioncomprises a material selected from the group consisting of a ceramic, aglass, a metal, a polymer, and a combination thereof.

Item 140. The method of item 135, wherein the first compositioncomprises a material selected from the group consisting of an oxide, acarbide, a nitride, a boride, an oxycarbide, oxynitride, oxyboride, anda combination thereof.

Item 141. The method of item 135, wherein the first compositioncomprises alumina.

Item 142. The method of item 135, wherein the second compositioncomprises a material selected from the group consisting of organicmaterial, inorganic material, and a combination thereof.

Item 143. The method of item 135, wherein the second compositioncomprises a material selected from the group consisting of a ceramic, aglass, a metal, a polymer, and a combination thereof.

Item 144. The method of item 135, wherein the second compositioncomprises a material selected from the group consisting of an oxide, acarbide, a nitride, a boride, an oxycarbide, oxynitride, oxyboride, anda combination thereof.

Item 145. The method of item 135, wherein the second compositioncomprises alumina.

Item 146. The method of item 106, wherein the second print materialincludes a solid, a powder, a solution, a mixture, a liquid, a slurry, agel, a binder, and a combination thereof.

Item 147. The method of item 1, further comprising forming the bodyaccording to a digital model.

Item 148. The method of any one of items 2 and 147, further comprisingcomparing at least a portion of the body to the digital model.

Item 149. The method of item 148, wherein comparing includes measuringat least a portion of the body and comparing it to a correspondingdimension of the digital model.

Item 150. The method of item 148, wherein comparing is conducted duringforming.

Item 151. The method of item 148, wherein comparing is conducted afterforming.

Item 152. The method of any one of items 2 and 147, further comprisingcreating a plurality of digital cross-sections of the digital model.

Item 153. The method of item 152, further comprising: depositing a firstportion of the body at a first time, the first portion corresponding toa first cross-section of the plurality of cross-sections of the digitalmodel; depositing a second portion of the body distinct from the firstportion at a second time different than the first time, the secondportion corresponding to a second cross-section of the plurality ofcross-sections of the digital model.

Item 154. The method of item 152, further comprising using the pluralityof digital cross-sections as a guide for depositing a plurality ofdiscrete portions.

Item 155. The method of item 1, wherein the additive manufacturingprocess defines a process of compiling discrete portions to form asub-portion.

Item 156. The method of item 155, further comprising compiling aplurality of sub-portions to form the body of the shaped abrasiveparticle.

Item 157. The method of any one of items 1 and 2, further comprising asubtractive process.

Item 158. The method of item 157, wherein the subtractive process isconducted after forming a body of a precursor shaped abrasive particle.

Item 159. The method of item 157, wherein the subtractive processincludes removing at least a portion of the material used to form aprecursor shaped abrasive particle.

Item 160. The method of item 157, wherein the subtractive processincludes forming at least one opening within a portion of the body.

Item 161. The method of item 157, wherein the subtractive processincludes forming an aperture through a portion of the body.

Item 162. The method of item 157, wherein the subtractive processincludes heating to remove a portion of the body.

Item 163. The method of item 162, wherein heating comprises volatilizingat least a portion of the body.

Item 164. The method of any one of items 1 and 2, further comprising atleast one process of modifying a portion of the body including melting,selective laser melting, sintering, selective sintering, direct metallaser sintering, selective laser sintering, particle beam modification,electron beam melting, fused deposition modeling, curing, and acombination thereof.

Item 165. The method of any one of items 1 and 2, wherein formingcomprises prototype printing of the body of the shaped abrasiveparticle.

Item 166. The method of any one of items 1 and 2, wherein formingcomprises laminated object manufacturing.

Item 167. The method of any one of items 1 and 2, wherein the bodycomprises a three-dimensional shape including a body length (Lb), a bodywidth (Wb), and a body thickness (Tb), and wherein Lb≥Wb, Lb≥Tb, andWb≥Tb.

Item 168. The method of item 167, wherein the body comprises a primaryaspect ratio (Lb:Wb) of at least about 1:1 or at least about 2:1 or atleast about 3:1 or at least about 5:1 or at least about 10:1, and notgreater than about 1000:1.

Item 169. The method of item 167, wherein the body comprises a secondaryaspect ratio (Lb:Tb) of at least about 1:1 or at least about 2:1 or atleast about 3:1 or at least about 5:1 or at least about 10:1, and notgreater than about 1000:1.

Item 170. The method of item 167, wherein the body comprises a tertiaryaspect ratio (Wb:Tb) of at least about 1:1 or at least about 2:1 or atleast about 3:1 or at least about 5:1 or at least about 10:1, and notgreater than about 1000:1.

Item 171. The method of item 167, wherein at least one of the bodylength (Lb), the body width (Wb), and the body thickness (Tb) has anaverage dimension of at least about 0.1 microns or at least about 1micron or at least about 10 microns or at least about 50 microns or atleast about 100 microns or at least about 150 microns or at least about200 microns or at least about 400 microns or at least about 600 micronsor at least about 800 microns or at least about 1 mm, and not greaterthan about 20 mm or not greater than about 18 mm or not greater thanabout 16 mm or not greater than about 14 mm or not greater than about 12mm or not greater than about 10 mm or not greater than about 8 mm or notgreater than about 6 mm or not greater than about 4 mm.

Item 172. The method of item 167, wherein the body comprises across-sectional shape in a plane defined by the body length and the bodywidth selected from the group consisting of triangular, quadrilateral,rectangular, trapezoidal, pentagonal, hexagonal, heptagonal, octagonal,ellipsoids, Greek alphabet characters, Latin alphabet characters,Russian alphabet characters, and a combination thereof.

Item 173. The method of item 167, wherein the body comprises across-sectional shape in a plane defined by the body length and the bodythickness selected from the group consisting of triangular,quadrilateral, rectangular, trapezoidal, pentagonal, hexagonal,heptagonal, octagonal, ellipsoids, Greek alphabet characters, Latinalphabet characters, Russian alphabet characters, and a combinationthereof.

Item 174. The method of any one of items 1 and 2, wherein the bodycomprises a three-dimensional shape selected from the group consistingof a polyhedron, a pyramid, an ellipsoid, a sphere, a prism, a cylinder,a cone, a tetrahedron, a cube, a cuboid, a rhombohedron, a truncatedpyramid, a truncated ellipsoid, a truncated sphere, a truncated cone, apentahedron, a hexahedron, a heptahedron, an octahedron, a nonahedron, adecahedron, Greek alphabet characters, Latin alphabet characters,Russian alphabet characters, and a combination thereof.

Item 175. The method of any one of items 1 and 2, further comprisingforming a plurality of shaped abrasive particles, wherein each of theshaped abrasive particles of the plurality of shaped abrasive particleshave a body having a body length (Lb), a body width (Wb), and a bodythickness (Tb).

Item 176. The method of item 175, wherein the plurality of shapedabrasive particles have at least one of: a body length variation of notgreater than about 50%; a body width variation of not greater than about50%; and a body thickness variation of not greater than about 50%.

Item 177. The method of any one of items 1 and 2, wherein the body has afirst major surface, a second major surface, and at least one sidesurface extending between the first major surface and the second majorsurface.

Item 178. The method of any one of items 1 and 2, wherein the bodycomprises a percent flashing not greater than about 40% or not greaterthan about 20% or not greater than about 10% or not greater than about4%, wherein the body is essentially free of flashing.

Item 179. The method of any one of items 1 and 2, wherein the body isessentially free of a binder, wherein the body is essentially free of anorganic material.

Item 180. The method of any one of items 1 and 2, wherein the bodycomprises a polycrystalline material, wherein the polycrystallinematerial comprises grains, wherein the grains are selected from thegroup of materials consisting of nitrides, oxides, carbides, borides,oxynitrides, diamond, and a combination thereof, wherein the grainscomprise an oxide selected from the group of oxides consisting ofaluminum oxide, zirconium oxide, titanium oxide, yttrium oxide, chromiumoxide, strontium oxide, silicon oxide, and a combination thereof,wherein the grains comprise alumina, wherein the grains consistessentially of alumina.

Item 181. The method of any one of items 1 and 2, wherein the bodyconsists essentially of alumina.

Item 182. The method of any one of items 1 and 2, wherein the body isformed from a seeded sol gel.

Item 183. The method of any one of items 1 and 2, wherein the bodycomprises a polycrystalline material having an average grain size notgreater than about 1 micron.

Item 184. The method of any one of items 1 and 2, wherein the body is acomposite comprising at least about 2 different types of compositions.

Item 185. The method of any one of items 1 and 2, wherein the bodycomprises an additive, wherein the additive comprises an oxide, whereinthe additive comprises a metal element, wherein the additive comprises arare-earth element.

Item 186. The method of item 185, wherein the additive comprises adopant material, wherein the dopant material includes an elementselected from the group consisting of an alkali element, an alkalineearth element, a rare earth element, a transition metal element, and acombination thereof, wherein the dopant material comprises an elementselected from the group consisting of hafnium, zirconium, niobium,tantalum, molybdenum, vanadium, lithium, sodium, potassium, magnesium,calcium, strontium, barium, scandium, yttrium, lanthanum, cesium,praseodymium, chromium, cobalt, iron, germanium, manganese, nickel,titanium, zinc, and a combination thereof.

Item 187. A method of forming a fixed abrasive comprising: forming aplurality of shaped abrasive particles on a substrate, wherein each ofthe shaped abrasive particles of the plurality of shaped abrasiveparticles have a body formed by an additive manufacturing process.

Item 188. The method of item 187, wherein forming is conducted directlyoverlying the substrate.

Item 189. The method of item 187, wherein forming is conducted directlyon at least a portion of a bonding layer overlying the substrate,wherein the bonding layer comprises a material selected from the groupconsisting of an inorganic material, a vitreous material, a crystallinematerial, an organic material, a resin material, a metal material, ametal alloy, and a combination thereof.

Item 190. The method of item 187, wherein the substrate is translatedthrough a forming zone, wherein in the forming zone at least one shapedabrasive particle of the plurality of shaped abrasive particles isformed overlying the substrate.

Item 191. The method of item 187, wherein translation includes a steppedtranslation process.

Item 192. The method of item 187, wherein the body of each of the shapedabrasive particles of the plurality of shaped abrasive particles isformed according to a digital model.

Item 193. The method of item 187, wherein the additive manufacturingprocess comprises: depositing a first print material as a first portionof the body of each of the shaped abrasive particles of the plurality ofshaped abrasive particles at a first time; and depositing a second printmaterial as a second portion of the body of each of the shaped abrasiveparticles of the plurality of shaped abrasive particles at a second timedifferent than the first time.

Item 194. The method of item 193, further comprising preferentiallymodifying one of the first portion and second portion to join the firstportion and second portion and form a subsection of the body of theshaped abrasive particle.

1 Item 95. The method of item 187, wherein the plurality of shapedabrasive particles are formed at a predetermined location on thesubstrate.

Item 196. The method of item 187, further comprising placing each of theshaped abrasive particles of the plurality of shaped abrasive particleson the substrate, wherein the placing is conducted simultaneously withforming the body of each of the shaped abrasive particles of theplurality of shaped abrasive particles.

Item 197. The method of item 187, further comprising orienting each ofthe shaped abrasive particles of the plurality of shaped abrasiveparticles relative to the substrate.

Item 198. The method of item 197, wherein orienting and forming areconducted simultaneously.

Item 199. The method of item 187, wherein at least about 55% of theplurality of shaped abrasive particles are oriented in a sideorientation.

Item 200. The method of item 187, wherein the plurality of shapedabrasive particles define an open coat, wherein the plurality of shapedabrasive particles of the first portion define a closed coat, whereinthe open coat comprises a coating density of not greater than about 70particles/cm².

Item 201. The method of item 187, wherein the substrate comprises awoven material, wherein the substrate comprises a non-woven material,wherein the substrate comprises an organic material, wherein thesubstrate comprises a polymer, wherein the substrate comprises amaterial selected from the group consisting of cloth, paper, film,fabric, fleeced fabric, vulcanized fiber, woven material, non-wovenmaterial, webbing, polymer, resin, phenolic resin, phenolic-latex resin,epoxy resin, polyester resin, urea formaldehyde resin, polyester,polyurethane, polypropylene, polyimides, and a combination thereof.

Item 202. The method of item 187, wherein the substrate comprises anadditive chosen from the group consisting of catalysts, coupling agents,curants, anti-static agents, suspending agents, anti-loading agents,lubricants, wetting agents, dyes, fillers, viscosity modifiers,dispersants, defoamers, and grinding agents.

Item 203. The method of item 187, further comprising an adhesive layeroverlying the substrate, wherein the adhesive layer comprises a makecoat, wherein the make coat overlies the substrate, wherein the makecoat is bonded directly to a portion of the substrate, wherein the makecoat comprises an organic material, wherein the make coat comprises apolymeric material, wherein the make coat comprises a material selectedfrom the group consisting of polyesters, epoxy resins, polyurethanes,polyamides, polyacrylates, polymethacrylates, poly vinyl chlorides,polyethylene, polysiloxane, silicones, cellulose acetates,nitrocellulose, natural rubber, starch, shellac, and a combinationthereof.

Item 204. The method of item 203, wherein the adhesive layer comprises asize coat, wherein the size coat overlies a portion of the plurality ofshaped abrasive particles, wherein the size coat overlies a make coat,wherein the size coat is bonded directly to a portion of the pluralityof shaped abrasive particles, wherein the size coat comprises an organicmaterial, wherein the size coat comprises a polymeric material, whereinthe size coat comprises a material selected from the group consisting ofpolyesters, epoxy resins, polyurethanes, polyamides, polyacrylates,polymethacrylates, poly vinyl chlorides, polyethylene, polysiloxane,silicones, cellulose acetates, nitrocellulose, natural rubber, starch,shellac, and a combination thereof.

Item 205. A shaped abrasive particle comprising a body having at leastone major surface having a self-similar feature.

Item 206. A shaped abrasive particle comprising a body having at leastone peripheral ridge extending around at least a portion of a sidesurface of the body.

Item 207. A shaped abrasive particle comprising a body having at leastone major surface defining a concave stepped surface.

Item 208. A shaped abrasive particle comprising a body having at leastone transverse ridge extending along at least two surfaces and anadjoining edge between the at least two surfaces.

Item 209. A shaped abrasive particle comprising a body having a cornerincluding a plurality of microprotrusions extending from the corner.

Item 210. A shaped abrasive particle comprising a body including asurface comprising a scalloped topography.

Item 211. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein body comprises a corner roundness of notgreater than about 250 microns or not greater than about 220 microns ornot greater than about 200 microns or not greater than about 180 micronsor not greater than about 160 microns or not greater than about 140microns or not greater than about 120 microns or not greater than about100 microns or not greater than about 90 microns or not greater thanabout 80 microns or not greater than about 70 microns or not greaterthan about 60 microns or not greater than about 50 microns or notgreater than about 40 microns or not greater than about 30 microns ornot greater than about 20 microns.

Item 212. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210, wherein body comprises a corner roundness of atleast about 0.1 microns or at least about 0.5 microns.

Item 213. The shaped abrasive particle of any one of items 206, 207,208, 209, and 210, wherein the body comprises a major surface includinga self-similar feature.

Item 214. The shaped abrasive particle of any one of items 205 and 213,wherein the self-similar feature comprises an arrangement oftwo-dimensional shapes having substantially the same two-dimensionalshape of the periphery of the major surface.

Item 215. The shaped abrasive particle of any one of items 205 and 213,wherein the major surface has a two-dimensional shape selected from thegroup consisting of regular polygons, irregular polygons, irregularshapes, triangles, quadrilaterals, rectangles, trapezoids, pentagons,hexagons, heptagons, octagons, ellipses, Greek alphabet characters,Latin alphabet characters, Russian alphabet characters, and acombination thereof.

Item 216. The shaped abrasive particle of any one of items 205 and 213,wherein the major surface comprises a triangular two-dimensional shape.

Item 217. The shaped abrasive particle of any one of items 205 and 213,wherein the self-similar feature comprises a plurality of triangulartwo-dimensional shapes nested within each other.

Item 218. The shaped abrasive particle of any one of items 205, 207,208, 209, and 210, wherein the body has at least one peripheral ridgeextending around at least a portion of a side surface of the body.

Item 219. The shaped abrasive particle of any one of items 206 and 218,wherein the at least one peripheral ridge extends around a majority ofthe side surface of the body.

Item 220. The shaped abrasive particle of any one of items 206 and 218,wherein the at least one peripheral ridge extends around an entire sidesurface of the body.

Item 221. The shaped abrasive particle of any one of items 206 and 218,wherein the at least one peripheral ridge extends around the sidesurface of the body without intersecting a major surface.

Item 222. The shaped abrasive particle of any one of items 206 and 218,wherein the at least one peripheral ridge intersects at least twosurfaces and an edge of the body.

Item 223. The shaped abrasive particle of any one of items 206 and 218,wherein the body comprises a length (l), a width (w), and a thickness(t), wherein 1≥w≥t, and the at least one peripheral ridge extendsperipherally around a side surface of the body extending between majorsurfaces.

Item 224. The shaped abrasive particle of any one of items 206 and 218,wherein the at least one peripheral ridge comprises a depth that is notgreater than about 0.8t, wherein “t” is a thickness of the body, notgreater than about 0.7t or not greater than about 0.6t or not greaterthan about 0.5t or not greater than about 0.4t or not greater than about0.3t or not greater than about 0.2t or not greater than about 0.18t ornot greater than about 0.16t or not greater than about 0.15t or notgreater than about 0.14t or not greater than about 0.12t or not greaterthan about 0.1t or not greater than about 0.09t or not greater thanabout 0.08t or not greater than about 0.07t or not greater than about0.06t or not greater than about 0.05t.

Item 225. The shaped abrasive particle of any one of items 206 and 218,wherein the at least one peripheral ridge comprises a depth that is atleast about 0.001t, wherein “t” is a thickness of the body, at leastabout 0.01t.

Item 226. The shaped abrasive particle of any one of items 205, 206,208, 209, and 210, wherein the body has at least one major surfacedefining a concave, stepped surface.

Item 227. The shaped abrasive particle of any one of items 207 and 226,wherein the concave stepped surface defines a thickness at the midpointof the major surface that is less than a thickness of the body at anedge.

Item 228. The shaped abrasive particle of any one of items 207 and 226,wherein concave stepped surface comprises a plurality of flats andrisers, wherein the flats extend substantially parallel to the plane ofthe major surface and the risers extend substantially perpendicular tothe plane of the major surface.

Item 229. The shaped abrasive particle of item 228, wherein the flatshave an average width (wf) that is not greater than about 0.8(l),wherein “l” defines a length of the body, not greater than about 0.5(l)or not greater than about 0.4(l) or not greater than about 0.3(l) or notgreater than about 0.2(l) or not greater than about 0.1(l) or notgreater than about 0.09(l) or not greater than about 0.08(l).

Item 230. The shaped abrasive particle of item 228, wherein the flatshave an average width (wf) that is at least about 0.001(l), wherein “l”defines a length of the body, at least about 0.005(l) or at least about0.01(l).

Item 231. The shaped abrasive particle of item 228, wherein the risershave an average height (hr) that is not greater than about 0.2(l),wherein “l” defines a length of the body, not greater than about 0.15(l)or not greater than about 0.1(l) or not greater than about 0.05(l) ornot greater than about 0.02(l).

Item 232. The shaped abrasive particle of item 228, wherein the risershave an average height (hr) that is at least about 0.0001(l) wherein “l”defines a length of the body, at least about 0.0005(l).

Item 233. The shaped abrasive particle of item 228, wherein the flatshave an average width that is greater than an average height of therisers, wherein the average height of the risers (hr) is not greaterthan about 0.95(wf), wherein “wf” defines an average width of the flats,not greater than about 0.9(wf) or not greater than about 0.8(wf) or notgreater than about 0.7(wf) or not greater than about 0.5(wf) or notgreater than about 0.3(wf) or not greater than about 0.2(wf) or notgreater than about 0.1(wf).

Item 234. The shaped abrasive particle of item 228, wherein the averageheight of the risers is at least about 0.0001(wf), wherein “wf” definesan average width of the flats, at least about 0.001(wf).

Item 235. The shaped abrasive particle of any one of items 205, 206,208, 209, and 210, wherein the body has at least one major surfacedefining a convex, stepped surface defining a thickness at the midpointof the major surface that is greater than a thickness of the body at anedge.

Item 236. The shaped abrasive particle of any one of items 205, 206,207, 209, and 210, wherein the body comprises at least one transverseridge extending along at least two surfaces and an adjoining edgebetween the at least two surfaces.

Item 237. The shaped abrasive particle of any one of items 208 and 236,wherein the at least one transverse ridge extends over at least threesurfaces and at least two adjoining edges between the at least threesurfaces.

Item 238. The shaped abrasive particle of any one of items 208 and 236,wherein the body comprises a plurality of transverse ridges, each of thetransverse ridges of the plurality of transverse ridges extendingparallel to each other around at least a portion of the periphery of thebody.

Item 239. The shaped abrasive particle of item 238, wherein at least oneof the transverse ridges of the plurality of transverse ridges has adifferent length relative to another transverse ridge of the pluralityof transverse ridges.

Item 240. The shaped abrasive particle of item 238, wherein each of thetransverse ridges of the plurality of transverse ridges have differentlengths relative to each other.

Item 241. The shaped abrasive particle of any one of items 205, 206,207, 208, and 210, wherein the body comprises a corner including aplurality of microprotrusions extending from the corner.

Item 242. The shaped abrasive particle of any one of items 209 and 241,wherein the microprotrusions define a plurality of discrete cornerprotrusions separated by a plurality of ridges.

Item 243. The shaped abrasive particle of item 242, wherein theplurality of discrete corner protrusions have a plurality of differentcontours relative to each other.

Item 244. The shaped abrasive particle of item 242, wherein at least twodiscrete corner protrusions have a different corner radius relative toeach other.

Item 245. The shaped abrasive particle of item 242, wherein at least twodiscrete corner protrusions define a step having a lateral shiftrelative to each other.

Item 246. The shaped abrasive particle of any one of items 209 and 241,wherein the corner roundness at an upper surface is different than acorner roundness at a bottom surface, and wherein the upper surface hasa lower surface area than the bottom surface.

Item 247. The shaped abrasive particle of any one of items 209 and 241,wherein the microprotrusions define a serrated edge.

Item 248. The shaped abrasive particle of any one of items 205, 206,207, 208, and 209, wherein the body has a surface comprising a scallopedtopography.

Item 249. The shaped abrasive particle of any one of items 210 and 248,wherein the scalloped topography extends over a majority of a surfacearea of at least one surface of the body.

Item 250. The shaped abrasive particle of any one of items 210 and 248,wherein the scalloped topography extends over a majority of an entiresurface area of at least one surface of the body.

Item 251. The shaped abrasive particle of any one of items 210 and 248,wherein the scalloped topography defines a plurality of curvedprotrusions having ridges extending between the curved protrusions.

Item 252. The shaped abrasive particle of any one of items 210 and 248,wherein the scalloped topography includes a plurality of elongatedprotrusions, each protrusion having a length, a width, and a height,wherein each protrusion has an arcuate contour extending in thedirection of the width and the height.

Item 253. The shaped abrasive particle of item 252, wherein the lengthof each elongated protrusion extends substantially in the direction of alength of the body.

Item 254. The shaped abrasive particle of item 252, wherein the lengthof at least one elongated protrusion is at least about 0.8(l), wherein“l” is the length of the body, at least about 09(l) or at least about1(l).

Item 255. The shaped abrasive particle of item 252, wherein theplurality of elongated protrusions have an average height that is lessthan the average width (wep), wherein the average height of theplurality of elongated protrusion is not greater than about 0.9(wep) ornot greater than about 0.8(wep) or not greater than about 0.7(wep) ornot greater than about 0.6(wep) or not greater than about 0.5(wep) ornot greater than about 0.4(wep) or not greater than about 0.3(wep) ornot greater than about 0.2(wep) or not greater than about 0.1(wep).

Item 256. The shaped abrasive particle of item 255, wherein the averageheight of the plurality of elongated protrusions is not greater thanabout 500 microns or not greater than about 400 microns or not greaterthan about 300 microns or not greater than about 250 microns or notgreater than about 200 microns or not greater than about 150 microns ornot greater than about 100 microns or not greater than about 90 micronsor not greater than about 70 microns or not greater than about 50microns.

Item 257. The shaped abrasive particle of item 252, wherein theplurality of elongated protrusions comprises an average width that isless than the average length.

Item 258. The shaped abrasive particle of item 252, wherein plurality ofelongated protrusions have an average width that is less than the length(l) of the body, wherein the average width of the plurality of elongatedprotrusion is not greater than about 0.9(l) or not greater than about0.8(l) or not greater than about 0.7(l) or not greater than about 0.6(l)or not greater than about 0.5(l) or not greater than about 0.4(l) or notgreater than about 0.3(l) or not greater than about 0.2(l) or notgreater than about 0.1(l).

Item 259. The shaped abrasive particle of item 252, wherein the averagewidth of the plurality of elongated protrusion is at least about0.001(l) or at least about 0.01(l).

Item 260. The shaped abrasive particle of item 252, wherein the averagewidth of the plurality of elongated protrusions is not greater thanabout 500 microns or not greater than about 400 microns or not greaterthan about 300 microns or not greater than about 250 microns or notgreater than about 200 microns.

Item 261. The shaped abrasive particle of any one of items 210 and 248,wherein the scalloped topography intersects an edge defining at leastone corner of the body and defines an edge having a serrated contouralong the length of the edge.

Item 262. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the body comprises at least 4 majorsurfaces joined together at common edges.

Item 263. The shaped abrasive particle of item 262, wherein the at least4 major surfaces have substantially the same surface area.

Item 264. The shaped abrasive particle of item 262, wherein the bodycomprises a tetrahedral shape.

Item 265. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the body comprises a three-dimensionalshape selected from the group consisting of a polyhedron, a pyramid, anellipsoid, a sphere, a prism, a cylinder, a cone, a tetrahedron, a cube,a cuboid, a rhombohedron, a truncated pyramid, a truncated ellipsoid, atruncated sphere, a truncated cone, a pentahedron, a hexahedron, aheptahedron, an octahedron, a nonahedron, a decahedron, Greek alphabetcharacters, Latin alphabet characters, Russian alphabet characters, avolcano shape, monostatic shape, and a combination thereof.

Item 266. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the body comprises a three-dimensionalshape including a body length (Lb), a body width (Wb), and a bodythickness (Tb), and wherein Lb≥Wb, Lb≥Tb, and Wb≥Tb.

Item 267. The shaped abrasive particle of item 266, wherein the bodycomprises a primary aspect ratio (Lb:Wb) of at least about 1:1 or atleast about 2:1 or at least about 3:1 or at least about 5:1 or at leastabout 10:1, and not greater than about 1000:1.

Item 268. The shaped abrasive particle of item 266, wherein the bodycomprises a secondary aspect ratio (Lb:Tb) of at least about 1:1 or atleast about 2:1 or at least about 3:1 or at least about 5:1 or at leastabout 10:1, and not greater than about 1000:1.

Item 269. The shaped abrasive particle of item 266, wherein the bodycomprises a tertiary aspect ratio (Wb:Tb) of at least about 1:1 or atleast about 2:1 or at least about 3:1 or at least about 5:1 or at leastabout 10:1, and not greater than about 1000:1.

Item 270. The shaped abrasive particle of item 266, wherein the bodycomprises a cross-sectional shape in a plane defined by the body lengthand the body width selected from the group consisting of triangular,quadrilateral, rectangular, trapezoidal, pentagonal, hexagonal,heptagonal, octagonal, ellipsoids, Greek alphabet characters, Latinalphabet characters, Russian alphabet characters, and a combinationthereof.

Item 271. The shaped abrasive particle of item 266, wherein the bodycomprises a cross-sectional shape in a plane defined by the body lengthand the body thickness selected from the group consisting of triangular,quadrilateral, rectangular, trapezoidal, pentagonal, hexagonal,heptagonal, octagonal, ellipsoids, Greek alphabet characters, Latinalphabet characters, Russian alphabet characters, and a combinationthereof.

Item 272. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the body is essentially free of a binder,wherein the body is essentially free of an organic material.

Item 273. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the body comprises a polycrystallinematerial, wherein the polycrystalline material comprises grains, whereinthe grains are selected from the group of materials consisting ofnitrides, oxides, carbides, borides, oxynitrides, diamond, and acombination thereof, wherein the grains comprise an oxide selected fromthe group of oxides consisting of aluminum oxide, zirconium oxide,titanium oxide, yttrium oxide, chromium oxide, strontium oxide, siliconoxide, and a combination thereof, wherein the grains comprise alumina,wherein the grains consist essentially of alumina.

Item 274. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the body is formed from a seeded sol gel.

Item 275. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the body comprises a polycrystallinematerial having an average grain size not greater than about 1 micron.

Item 276. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the body is a composite comprising atleast about 2 different types of compositions.

Item 277. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the body comprises an additive, whereinthe additive comprises an oxide, wherein the additive comprises a metalelement, wherein the additive comprises a rare-earth element.

Item 278. The shaped abrasive particle of item 277, wherein the additivecomprises a dopant material, wherein the dopant material includes anelement selected from the group consisting of an alkali element, analkaline earth element, a rare earth element, a transition metalelement, and a combination thereof, wherein the dopant materialcomprises an element selected from the group consisting of hafnium,zirconium, niobium, tantalum, molybdenum, vanadium, lithium, sodium,potassium, magnesium, calcium, strontium, barium, scandium, yttrium,lanthanum, cesium, praseodymium, chromium, cobalt, iron, germanium,manganese, nickel, titanium, zinc, and a combination thereof.

Item 279. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the body is coupled to a substrate aspart of a fixed abrasive, wherein the fixed abrasive article is selectedfrom the group consisting of a bonded abrasive article, a coatedabrasive article, and a combination thereof.

Item 280. The shaped abrasive particle of item 279 wherein the substrateis a backing, wherein the backing comprises a woven material, whereinthe backing comprises a non-woven material, wherein the backingcomprises an organic material, wherein the backing comprises a polymer,wherein the backing comprises a material selected from the groupconsisting of cloth, paper, film, fabric, fleeced fabric, vulcanizedfiber, woven material, non-woven material, webbing, polymer, resin,phenolic resin, phenolic-latex resin, epoxy resin, polyester resin, ureaformaldehyde resin, polyester, polyurethane, polypropylene, polyimides,and a combination thereof.

Item 281. The shaped abrasive particle of item 280, wherein the backingcomprises an additive selected from the group consisting of catalysts,coupling agents, curants, anti-static agents, suspending agents,anti-loading agents, lubricants, wetting agents, dyes, fillers,viscosity modifiers, dispersants, defoamers, and grinding agents.

Item 282. The shaped abrasive particle of item 280, further comprisingan adhesive layer overlying the backing, wherein the adhesive layercomprises a make coat, wherein the make coat overlies the backing,wherein the make coat is bonded directly to a portion of the backing,wherein the make coat comprises an organic material, wherein the makecoat comprises a polymeric material, wherein the make coat comprises amaterial selected from the group consisting of polyesters, epoxy resins,polyurethanes, polyamides, polyacrylates, polymethacrylates, poly vinylchlorides, polyethylene, polysiloxane, silicones, cellulose acetates,nitrocellulose, natural rubber, starch, shellac, and a combinationthereof.

Item 283. The shaped abrasive particle of item 282, wherein the adhesivelayer comprises a size coat, wherein the size coat overlies a portion ofthe plurality of shaped abrasive particles, wherein the size coatoverlies a make coat, wherein the size coat is bonded directly to aportion of the plurality of shaped abrasive particles, wherein the sizecoat comprises an organic material, wherein the size coat comprises apolymeric material, wherein the size coat comprises a material selectedfrom the group consisting of polyesters, epoxy resins, polyurethanes,polyamides, polyacrylates, polymethacrylates, polyvinyl chlorides,polyethylene, polysiloxane, silicones, cellulose acetates,nitrocellulose, natural rubber, starch, shellac, and a combinationthereof.

Item 284. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the shaped abrasive particle is part of aplurality of a first type of shaped abrasive particles, wherein amajority of the first type of shaped abrasive particles are coupled to abacking in an open coat, wherein the open coat comprises a coatingdensity of not greater than about 70 particles/cm² or not greater thanabout 65 particles/cm² or not greater than about 60 particles/cm² or notgreater than about 55 particles/cm² or not greater than about 50particles/cm² or at least about 5 particles/cm² or at least about 10particles/cm².

Item 285. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the shaped abrasive particle is part of aplurality of a first type of shaped abrasive particles, wherein amajority of the first type of shaped abrasive particles are coupled to abacking in a closed coat, wherein having a closed coat of the blend ofshaped abrasive particles on a backing, wherein the closed coatcomprises a coating density of at least about 75 particles/cm² or atleast about 80 particles/cm² or at least about 85 particles/cm² or atleast about 90 particles/cm² or at least about 100 particles/cm².

Item 286. The shaped abrasive particle of any one of items 205, 206,207, 208, 209, and 210 wherein the shaped abrasive particle is part of ablend including a plurality of a first type of shaped abrasive particlesand a third type of abrasive particle, wherein the third type ofabrasive particle comprises a shaped abrasive particle, wherein thethird type of abrasive particle comprises a diluent type of abrasiveparticle, wherein the diluent type of abrasive particle comprises anirregular shape.

Item 287. The shaped abrasive particle of item 286, wherein the blend ofabrasive particles comprises a plurality of shaped abrasive particles,and wherein each shaped abrasive particle of the plurality of shapedabrasive particles is arranged in a controlled orientation relative to abacking, the controlled orientation including at least one of apredetermined rotational orientation, a predetermined lateralorientation, and a predetermined longitudinal orientation.

Item 288. A method of forming a shaped abrasive particle using a lowpressure injection molding process.

Item 289. The method of item 288, wherein the low pressure injectionmolding includes filling a mold with a mold material using laminar flowconditions.

Item 290. The method of item 288, wherein the laminar flow conditionsare based on at least one of a rheology of the mold material, the shapeof the mold, mold material, and a combination thereof.

EXAMPLES Example 1

A print material was made by creating a mixture including 39 wt %boehmite and alpha alumina seeds in water. Nitric acid was added toadjust the pH of the mixture to 4. The print material was thentransferred to a container, de-aired using a vacuum pump, and aged atroom temperature for up to 30 days or until the rheological propertieswere sufficient for printing. The print material was then loaded into adeposition assembly of a robocasting unit, commercially available as EFDNordson® Ultra TT 525 having a Tungsten Palm OS® controller and EFD 1.2software. The deposition assembly includes a nozzle having a nozzlewidth of 100 μm, a nozzle tip length of approximately 6.35 mm or 3 mm.The print material had a static yield stress of approximately 750 Pa, adynamic yield stress of approximately 450 Pa. The print material was ashear thinning mixture with an apparent viscosity of 9000 Pa s at ashear rate of 100 s⁻¹.

The height of the nozzle and the tactile height sensor were carefullyadjusted so that the height measurements used by the printer wereaccurate. An initial line of print material was deposited to expel airand adjust the deposition pressure, deposition rate, deposition volume,and dispense gap. Certain process parameters such as the depositionrate, deposition pressure, and dispense gap were evaluated and adjustedbased on the rheological characteristics of the print material until theprinted line had approximately the same width as the nozzle width. Thepressure was approximately 0.5 MPa (70 psi), the deposition rate wasapproximately 3 mm/s, and the dispense gap was approximately 100 μm.

A program for forming a shaped abrasive particle having a triangularshape including deposition of 6 layers of the same size was loaded ontothe controller. The filling pattern included deposition of a first layerhaving a triangular two-dimensional shape using an outside-in “escargot”process. The premove delay was 0.1 seconds. A second layer was thenformed overlying the first layer. The nozzle was moved vertically upward100 μm above the stop position of the first layer. The second layer wasthen formed having a triangular two-dimensional shape and was formedusing a filling pattern based on an inside-out process. The premovedelay was 0.3 seconds. Four additional layers were formed on top of eachother using the alternating outside-in and inside-out process until 6layers were formed.

The body was dried in ambient conditions and sintered at approximately1250° C. for 90 minutes. The shaped abrasive particle of FIG. 20 isrepresentative of the shaped abrasive particle formed according toExample 1.

Example 2

A tetrahedral or pyramidal shaped abrasive particle was formed using thesame print material of Example 1. The robocasting parameters were thesame as Example 1 except that the nozzle width was 150 microns and thenozzle length was approximately 6.35 mm. Moreover, the filling processwas essentially the same as Example 1, except that the premove delay was0.2 seconds for layers formed using an inside-out filling process, andeach of the layers got successively smaller in size as the pyramidalshape was formed. The shaped abrasive particles were dried in ambientconditions and sintered at approximately 1250° C. for 90 minutes. Theshaped abrasive particle of FIGS. 28 and 29 is representative of ashaped abrasive particle formed according to Example 2.

Example 3

A volcano-shape, shaped abrasive particle was formed using the sameprint material of Example 2, except that the filling process is changedfor a final grouping of the layers, such as about the last 3 layers. Thefilling pattern uses an alternating outside-in and inside-out fillingprocess as described in Example 2, except that the final group of layerswere deposited around the periphery of the shape, but did not depositthe print material fully into the interior of the body to create theopening and volcano-shape. The shaped abrasive particles were dried inambient conditions and sintered at approximately 1250° C. for 90minutes. The shaped abrasive particle of FIG. 27 is representative of ashaped abrasive particle formed according to Example 3 including theopening 2709.

Certain references have demonstrated the formation of various objects ona centimeter scale by certain additive manufacturing techniques.However, these references are not directed to the formation of shapedabrasive particles having the features of the shaped abrasive particlesof the embodiments herein making them suitable for use as abrasives.Moreover, formation of shaped abrasive particles having the features anddimensions of the embodiments herein, which makes them suitable fortheir intended purpose, requires knowledge that is not readily availablefrom references disclosing formation of articles on a centimeter scale.The knowledge needed to migrate from centimeter scale technology tomillimeter or micron sized technology is non-trivial and was the resultof significant research. Benefits, other advantages, and solutions toproblems have been described above with regard to specific embodiments.However, the benefits, advantages, solutions to problems, and anyfeature(s) that may cause any benefit, advantage, or solution to occuror become more pronounced are not to be construed as a critical,required, or essential feature of any or all the items.

The shaped abrasive particles of the embodiments herein are suitable foruse in fixed abrasive articles, which may be used to create products invarious industries including metal working and fabrication industries,the automotive industry, building and construction materials, and thelike.

The specification and illustrations of the embodiments described hereinare intended to provide a general understanding of the structure of thevarious embodiments. The specification and illustrations are notintended to serve as an exhaustive and comprehensive description of allof the elements and features of apparatus and systems that use thestructures or methods described herein. Separate embodiments may also beprovided in combination in a single embodiment, and conversely, variousfeatures that are, for brevity, described in the context of a singleembodiment, may also be provided separately or in any subcombination.Further, reference to values stated in ranges includes each and everyvalue within that range. Many other embodiments may be apparent toskilled artisans only after reading this specification. Otherembodiments may be used and derived from the disclosure, such that astructural substitution, logical substitution, or another change may bemade without departing from the scope of the disclosure. Accordingly,the disclosure is to be regarded as illustrative rather thanrestrictive.

The foregoing description in combination with the figures is provided toassist in understanding the teachings disclosed herein. The followingdiscussion will focus on specific implementations and embodiments of theteachings. This focus is provided to assist in describing the teachingsand should not be interpreted as a limitation on the scope orapplicability of the teachings. However, other teachings can certainlybe used in this application.

As used herein, the terms “comprises,” “comprising,” “includes,”“including,” “has,” “having” or any other variation thereof, areintended to cover a non-exclusive inclusion. For example, a method,article, or apparatus that comprises a list of features is notnecessarily limited only to those features but may include otherfeatures not expressly listed or inherent to such method, article, orapparatus. Further, unless expressly stated to the contrary, “or” refersto an inclusive-or and not to an exclusive-or. For example, a conditionA or B is satisfied by any one of the following: A is true (or present)and B is false (or not present), A is false (or not present) and B istrue (or present), and both A and B are true (or present).

Also, the use of “a” or “an” is employed to describe elements andcomponents described herein. This is done merely for convenience and togive a general sense of the scope of the invention. This descriptionshould be read to include one or at least one and the singular alsoincludes the plural, or vice versa, unless it is clear that it is meantotherwise. For example, when a single item is described herein, morethan one item may be used in place of a single item. Similarly, wheremore than one item is described herein, a single item may be substitutedfor that more than one item.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. The materials, methods, andexamples are illustrative only and not intended to be limiting. To theextent not described herein, many details regarding specific materialsand processing acts are conventional and may be found in reference booksand other sources within the structural arts and correspondingmanufacturing arts.

What is claimed is:
 1. A method of forming a fixed abrasive comprising:forming a plurality of shaped abrasive particles on a substrate, whereineach of the shaped abrasive particles of the plurality of shapedabrasive particles have a body formed by an additive manufacturingprocess.
 2. The method of claim 1, wherein forming is conducted directlyoverlying the substrate.
 3. The method of claim 1, wherein forming isconducted directly on at least a portion of a bonding layer overlyingthe substrate, wherein the bonding layer comprises a material selectedfrom the group consisting of an inorganic material, a vitreous material,a crystalline material, an organic material, a resin material, a metalmaterial, a metal alloy, and a combination thereof.
 4. The method ofclaim 1, wherein the substrate is translated through a forming zone,wherein in the forming zone at least one shaped abrasive particle of theplurality of shaped abrasive particles is formed overlying thesubstrate.
 5. The method of claim 1, wherein translation includes astepped translation process.
 6. The method of claim 1, wherein the bodyof each of the shaped abrasive particles of the plurality of shapedabrasive particles is formed according to a digital model.
 7. The methodof claim 1, wherein the additive manufacturing process comprises:depositing a first print material as a first portion of the body of eachof the shaped abrasive particles of the plurality of shaped abrasiveparticles at a first time; and depositing a second print material as asecond portion of the body of each of the shaped abrasive particles ofthe plurality of shaped abrasive particles at a second time differentthan the first time.
 8. The method of claim 7, further comprisingpreferentially modifying one of the first portion and second portion tojoin the first portion and second portion and form a subsection of thebody of the shaped abrasive particle.
 9. The method of claim 1, whereinthe plurality of shaped abrasive particles are formed at a predeterminedlocation on the substrate.
 10. The method of claim 1, further comprisingplacing each of the shaped abrasive particles of the plurality of shapedabrasive particles on the substrate, wherein the placing is conductedsimultaneously with forming the body of each of the shaped abrasiveparticles of the plurality of shaped abrasive particles.
 11. The methodof claim 1, further comprising orienting each of the shaped abrasiveparticles of the plurality of shaped abrasive particles relative to thesubstrate.
 12. The method of claim 11, wherein orienting and forming areconducted simultaneously.
 13. The method of claim 1, wherein at leastabout 55% of the plurality of shaped abrasive particles are oriented ina side orientation.
 14. The method of claim 1, wherein the plurality ofshaped abrasive particles define an open coat.
 15. The method of claim14, wherein the open coat comprises a coating density of not greaterthan about 70 particles/cm².
 16. The method of claim 1, wherein thesubstrate comprises a material selected from the group consisting ofcloth, paper, film, fabric, fleeced fabric, vulcanized fiber, wovenmaterial, non-woven material, webbing, polymer, resin, phenolic resin,phenolic-latex resin, epoxy resin, polyester resin, urea formaldehyderesin, polyester, polyurethane, polypropylene, polyimides, and acombination thereof.
 17. The method of claim 1, wherein the bodycomprises a polycrystalline material.
 18. The method of claim 17,wherein the polycrystalline material comprises grains consisting ofnitrides, oxides, carbides, borides, oxynitrides, diamond, and acombination thereof, wherein the grains comprise an oxide selected fromthe group of oxides consisting of aluminum oxide, zirconium oxide,titanium oxide, yttrium oxide, chromium oxide, strontium oxide, siliconoxide, and a combination thereof.
 19. The method of claim 1, wherein thebody consists essentially of alumina.
 20. The method of claim 1, whereinthe body is essentially free of a binder.